Gas phase atmospheric bromine photochemistry
Journal of Geophysical Research - Atmospheres (1996)
- ISSN: 01480227
- DOI: 10.1029/95JD02463
Available from
David Lary's profile on Mendeley.
or
Abstract
This paper reviews the current knowledge of gas phase bromine photochemistry and presents a budget study of atmospheric bromine species. The effectiveness of the ozone catalytic loss cycles involving bromine is quantified by considering their chain length and effectiveness. The chain effectiveness is a new variable defined as the chain length multiplied by the rate of the cycle's rate-limiting step. The chain effectiveness enables a fair comparison of different catalytic cycles involving species which have very different concentrations. This analysis clearly shows that below 25 km the BrO/ClO and BrO/HO2 cycles are among the most important ozone destruction cycles.
Available from
David Lary's profile on Mendeley.
Page 1
Gas phase atmospheric bromine photochemistry
JOURNAL OF GEOPHYSICAL RESEARCH, VOL. 101, NO. D1, PAGES 1505-1516, JANUARY 20, 1996
Gas phase atmospheric bromine photochemistry
D. J. Lary
Centre for Atmospheric Science, Cambridge University, Cambridge, England
Abstract. This paper reviews the current knowledge of gas phase bromine
photochemistry and presents a budget study of atmospheric bromine species. The
effectiveness of the ozone catalytic loss cycles involving bromine is quantified by
considering their chain length and effectiveness. The chain effectiveness i a new
variable defined as the chain length multiplied by the rate of the cycle's rate-limiting
step. The chain effectiveness enables a fair comparison of different catalytic cycles
involving species which have very different concentrations. This analysis clearly
shows that below 25 km the BrO/C10 and BrO/HO2 cycles are among the most
important ozone destruction cycles.
Introduction
This paper is a review of gas phase bromine photo-
chemistry and is intended to complement the compan-
ion paper [Lary et al. this issue] which considers hetero-
geneous bromine photochemistry. Bromine enters the
atmosphere by a variety of natural and anthropogenic
processes. The three main bromine source gases that
can reach the stratosphere (i.e. are not removed from
the troposphere by rainout, reaction with OH or photol-
ysis) are CH3Br, CBrC1F2 and CBrF3. The most abun-
dant of these source gases is methyl bromide (CH3Br)
whose natural source is mainly due to oceanic biologi-
cal processes. In these, mainly algal, processes CH3Br
is formed together with other species such as CH2Br2,
CHBr3, CH2BrC1 and CHBrC12. The oceans are a sig-
nificant natural source of CH3Br [Singh et al., 1983].
Measurements of larger tropospheric northern henri-
sphere mixing ratios suggest a large land based north-
ern hemisphere source of CH3Br which could well be
anthropogenic [Penkett et al., 1985; Reeves and Pen-
kett, 1993]. The main industrial use of CH3Br is as a
fumigant, particularly for the treatment of soils. CH3Br
is also used in quarantine treatments and in insect and
rodent control.
The wide variety of CH3Br measurements made over
the last decade in different parts of the world [Berg et
al., 1984; Rasmussen and Khalil, 1984; Penkett et al.,
1985; Cicerone et al., 1988; Fabian et al., 1994; Kaye et
al., 1994] suggest hat the natural background concen-
tration of CH3Br in the troposphere is approximately
10 pptv. CH3Br concentrations of up to 15 pptv have
also been observed; these are likely to reflect the effect
of anthropogenic sources.
Copyright 1996 by the American Geophysical Union.
Paper number 95JD02463.
0148-0227 / 96 / 95 J D-02463505.00
The first study of atmospheric bromine chemistry
was by Yung et al. [1980], who pointed to the gen-
eral importance of atmospheric bromine chemistry and
to the catalytic destruction of ozone by the C10/BrO
cycle. Bromine has been shown to play a significant
role (m20%) in the formation of the ozone hole in polar
stratospheric regions [McElroy et al., 1986]. The contri-
butions to ozone loss from bromine reactions are largest
below about 20 km [e.g., Poulet et al., 1992; Garcia and
Solomon, 1994]. Bromine plays an important role in
stratospheric ozone depletion despite being much less
abundant than chlorine [World Meteorological Organi-
sation ( WMO), 1992].
When atmospheric bromine chemistry is compared
to chlorine chemistry, it can be seen that much more
bromine is present in the active forms Br and BrO
than chlorine is present in their counterparts C1 and
C10. Consequently, bromine has a greater potential
to destroy stratospheric ozone than does chlorine [e.g.
WMO, 1990,1992].
Section 2 describes the photochemical model used
in this study, which contains a detailed photochem-
istry scheme. Section 3 gives a budget study of atlllO-
spheric bromine species based on the current knowledge
of gas phase bromine chemistry. Se, ction 4 considers the
effectiveness of the various ozone-destroying catalytic
bromine cycles. Section 5 summarizes the main conclu-
sions.
Model Description
The column model used in this study is a version of
a new suite of models called AuTOCHEM. The model
included a total of 53 species. No family or photo-
chemical equilibrium assumptions are made. Of the
53 species, 51 species are integrated separae!y with
a 15 minute time step, namely: O(D), O(3p), 03,
N, NO, NO2, NO3, N2Os, HONO, HNO3, HNO3(s),
HO2NO2, C1, C12, C10, C1OO, OC10, C1202, C1NO2,
1505
Gas phase atmospheric bromine photochemistry
D. J. Lary
Centre for Atmospheric Science, Cambridge University, Cambridge, England
Abstract. This paper reviews the current knowledge of gas phase bromine
photochemistry and presents a budget study of atmospheric bromine species. The
effectiveness of the ozone catalytic loss cycles involving bromine is quantified by
considering their chain length and effectiveness. The chain effectiveness i a new
variable defined as the chain length multiplied by the rate of the cycle's rate-limiting
step. The chain effectiveness enables a fair comparison of different catalytic cycles
involving species which have very different concentrations. This analysis clearly
shows that below 25 km the BrO/C10 and BrO/HO2 cycles are among the most
important ozone destruction cycles.
Introduction
This paper is a review of gas phase bromine photo-
chemistry and is intended to complement the compan-
ion paper [Lary et al. this issue] which considers hetero-
geneous bromine photochemistry. Bromine enters the
atmosphere by a variety of natural and anthropogenic
processes. The three main bromine source gases that
can reach the stratosphere (i.e. are not removed from
the troposphere by rainout, reaction with OH or photol-
ysis) are CH3Br, CBrC1F2 and CBrF3. The most abun-
dant of these source gases is methyl bromide (CH3Br)
whose natural source is mainly due to oceanic biologi-
cal processes. In these, mainly algal, processes CH3Br
is formed together with other species such as CH2Br2,
CHBr3, CH2BrC1 and CHBrC12. The oceans are a sig-
nificant natural source of CH3Br [Singh et al., 1983].
Measurements of larger tropospheric northern henri-
sphere mixing ratios suggest a large land based north-
ern hemisphere source of CH3Br which could well be
anthropogenic [Penkett et al., 1985; Reeves and Pen-
kett, 1993]. The main industrial use of CH3Br is as a
fumigant, particularly for the treatment of soils. CH3Br
is also used in quarantine treatments and in insect and
rodent control.
The wide variety of CH3Br measurements made over
the last decade in different parts of the world [Berg et
al., 1984; Rasmussen and Khalil, 1984; Penkett et al.,
1985; Cicerone et al., 1988; Fabian et al., 1994; Kaye et
al., 1994] suggest hat the natural background concen-
tration of CH3Br in the troposphere is approximately
10 pptv. CH3Br concentrations of up to 15 pptv have
also been observed; these are likely to reflect the effect
of anthropogenic sources.
Copyright 1996 by the American Geophysical Union.
Paper number 95JD02463.
0148-0227 / 96 / 95 J D-02463505.00
The first study of atmospheric bromine chemistry
was by Yung et al. [1980], who pointed to the gen-
eral importance of atmospheric bromine chemistry and
to the catalytic destruction of ozone by the C10/BrO
cycle. Bromine has been shown to play a significant
role (m20%) in the formation of the ozone hole in polar
stratospheric regions [McElroy et al., 1986]. The contri-
butions to ozone loss from bromine reactions are largest
below about 20 km [e.g., Poulet et al., 1992; Garcia and
Solomon, 1994]. Bromine plays an important role in
stratospheric ozone depletion despite being much less
abundant than chlorine [World Meteorological Organi-
sation ( WMO), 1992].
When atmospheric bromine chemistry is compared
to chlorine chemistry, it can be seen that much more
bromine is present in the active forms Br and BrO
than chlorine is present in their counterparts C1 and
C10. Consequently, bromine has a greater potential
to destroy stratospheric ozone than does chlorine [e.g.
WMO, 1990,1992].
Section 2 describes the photochemical model used
in this study, which contains a detailed photochem-
istry scheme. Section 3 gives a budget study of atlllO-
spheric bromine species based on the current knowledge
of gas phase bromine chemistry. Se, ction 4 considers the
effectiveness of the various ozone-destroying catalytic
bromine cycles. Section 5 summarizes the main conclu-
sions.
Model Description
The column model used in this study is a version of
a new suite of models called AuTOCHEM. The model
included a total of 53 species. No family or photo-
chemical equilibrium assumptions are made. Of the
53 species, 51 species are integrated separae!y with
a 15 minute time step, namely: O(D), O(3p), 03,
N, NO, NO2, NO3, N2Os, HONO, HNO3, HNO3(s),
HO2NO2, C1, C12, C10, C1OO, OC10, C1202, C1NO2,
1505
Page 2
1506 LARY: GAS PHASE ATMOSPHERIC BROMINE PHOTOCHEMISTRY
C1ONO2, HC1, HCI(s), HOC1, H, OH, HO2, H202, CH,
CH302, CH302NO2, CHOOH, CHO, HCHO, HCO,
Br, Br2, BrO, BrONO2, BrONO, HBr, HOBr, BrC1,
H2, H20, H20(s), CO, CO2, CH4, N20, CH3Br and
CF2C12. 02 and N2 are included but not time inte-
grated. The version of AUTOCHEM used in this study
contains a total of 236 reactions, 129 bimolecular reac-
tions, 27 trimolecular reactions, 42 photochemical re-
actions and 38 heterogeneous reactions. The rate con-
stants for the reactions were taken from A tkinson ½t al.
[1992] and DeMote ½t al. [1994].
The time integration scheme used is an adaptive
timestep Burlisch-$toer scheme [$toer and Burlisch, 1980'
specifically designed for integration of stiff systems af-
ter Press et al. [1992]. The time integration package
is as accurate as the often used Gear [1971] package
but faster. Photolysis rates are calculated by using full
spherical geometry and multiple scattering as described
by Lary and Pyle [1992a,b] after Meier et al. [1982],
Nicolet et al. [1982] and Anderson [1983]. The average
photolysis rate over a model time step is calculated us-
ing 10 point gaussian quadrature as described by Press
et al. [1992].
AUTOCHEM has also been used to perform for the
first time four-dimensional variational analysis of chem-
ical species [Fisher and œary, 1995] and to examine
the effect of the reaction OH+C10 HCl+O9. on polar
ozone photochemistry [Lary et al., 1995].
Gas Phase Bromine Chemistry
This section examines the budgets of reactive bromine
species as predicted by our current understanding of the
gas phase kinetics of bromine. Figure 1 is a reaction
scheme of atmospheric bromine photochemistry. Her-
erogeneous nitrogen and chlorine reactions are consid-
ered in these calculations but not heterogeneous bromine
reactions. Heterogeneous bromine reactions are the
subject of the companion paper Lary et al. [this issue].
The reactive bromine species included in AUTOCHEM
are Br, Br2, BrO, BrONO, BrONO2, HBr, HOBr and
BrC1.
Figure 2 shows the calculated midlatitude photo-
chemical lifetimes of these species for local noon at
equinox, and Figure 3 shows the calculated midlatitude
partitioning of reactive bromine species for local noon
at equinox.
It can be seen from Figure 2 that in marked contrast
to their chlorine counterparts all of the bromine species
are short-lived. Figure 3 shows that typically the most
abundant inorganic bromine species in the lower strato-
sphere are BrO, BrONO. and HOBr. Each of the reac-
tive bromine species will now be considered in turn.
BrONO
BrONO has a photochemical ifetime of a few min-
utes throughout the sunlit middle atmosphere (the solid
squares in the right-hand panel of Figure 2). The rela-
tively short lifetime of BrONO is due to the photolysis
of BrONO2, which occurs in the visible region of the
spectrum. Consequently, BrONO is very close to pho-
tochemical steady state in the sunlit atmosphere. The
recent study of Burkholder et al. [1995] measured the
absorption cross section of BrONO. in the important
tail region between about 390 nm and 500 nm extend-
ing the previous measurements of Spencer and Rowland
[1978]. As pointed out by Burkholder et al. [1995], if
the products are BrO and NO then BrONO will not
be involved in catalytic ozone destruction. Photolysis
would merely reverse the formation of BrONO.. How-
O(3p), OH
NO, 0 3
HO2
HCHO /
(3p) NO2
h,, O(3P)
Figure 1. Schematic of atmospheric bromine photochemistry.
C1ONO2, HC1, HCI(s), HOC1, H, OH, HO2, H202, CH,
CH302, CH302NO2, CHOOH, CHO, HCHO, HCO,
Br, Br2, BrO, BrONO2, BrONO, HBr, HOBr, BrC1,
H2, H20, H20(s), CO, CO2, CH4, N20, CH3Br and
CF2C12. 02 and N2 are included but not time inte-
grated. The version of AUTOCHEM used in this study
contains a total of 236 reactions, 129 bimolecular reac-
tions, 27 trimolecular reactions, 42 photochemical re-
actions and 38 heterogeneous reactions. The rate con-
stants for the reactions were taken from A tkinson ½t al.
[1992] and DeMote ½t al. [1994].
The time integration scheme used is an adaptive
timestep Burlisch-$toer scheme [$toer and Burlisch, 1980'
specifically designed for integration of stiff systems af-
ter Press et al. [1992]. The time integration package
is as accurate as the often used Gear [1971] package
but faster. Photolysis rates are calculated by using full
spherical geometry and multiple scattering as described
by Lary and Pyle [1992a,b] after Meier et al. [1982],
Nicolet et al. [1982] and Anderson [1983]. The average
photolysis rate over a model time step is calculated us-
ing 10 point gaussian quadrature as described by Press
et al. [1992].
AUTOCHEM has also been used to perform for the
first time four-dimensional variational analysis of chem-
ical species [Fisher and œary, 1995] and to examine
the effect of the reaction OH+C10 HCl+O9. on polar
ozone photochemistry [Lary et al., 1995].
Gas Phase Bromine Chemistry
This section examines the budgets of reactive bromine
species as predicted by our current understanding of the
gas phase kinetics of bromine. Figure 1 is a reaction
scheme of atmospheric bromine photochemistry. Her-
erogeneous nitrogen and chlorine reactions are consid-
ered in these calculations but not heterogeneous bromine
reactions. Heterogeneous bromine reactions are the
subject of the companion paper Lary et al. [this issue].
The reactive bromine species included in AUTOCHEM
are Br, Br2, BrO, BrONO, BrONO2, HBr, HOBr and
BrC1.
Figure 2 shows the calculated midlatitude photo-
chemical lifetimes of these species for local noon at
equinox, and Figure 3 shows the calculated midlatitude
partitioning of reactive bromine species for local noon
at equinox.
It can be seen from Figure 2 that in marked contrast
to their chlorine counterparts all of the bromine species
are short-lived. Figure 3 shows that typically the most
abundant inorganic bromine species in the lower strato-
sphere are BrO, BrONO. and HOBr. Each of the reac-
tive bromine species will now be considered in turn.
BrONO
BrONO has a photochemical ifetime of a few min-
utes throughout the sunlit middle atmosphere (the solid
squares in the right-hand panel of Figure 2). The rela-
tively short lifetime of BrONO is due to the photolysis
of BrONO2, which occurs in the visible region of the
spectrum. Consequently, BrONO is very close to pho-
tochemical steady state in the sunlit atmosphere. The
recent study of Burkholder et al. [1995] measured the
absorption cross section of BrONO. in the important
tail region between about 390 nm and 500 nm extend-
ing the previous measurements of Spencer and Rowland
[1978]. As pointed out by Burkholder et al. [1995], if
the products are BrO and NO then BrONO will not
be involved in catalytic ozone destruction. Photolysis
would merely reverse the formation of BrONO.. How-
O(3p), OH
NO, 0 3
HO2
HCHO /
(3p) NO2
h,, O(3P)
Figure 1. Schematic of atmospheric bromine photochemistry.
Page 3
LARY: GAS PHASE ATMOSPHERIC BROMINE PHOTOCHEMISTRY 1507
10\"
40-
-
-
_
30-
_
_
_
20-
_
10\"
- Br - ' - Br2
---*--- BrO ,, BrONO
10 o 10' 102 103
I I tillIll I I IIIIII] I I IIIIIII I I IIIII1[
/
-
ß
100 10' 102 103
- BrONO2 -'- HBr
----- HOBr ,, BrCI
100 102 104
I IIIIIIII IIIIIIIII I IIIIIII I IIIIIIII I IIIIIIll I IIIII111 IIII
- 60
:,. , 40
11111111] I llllllll III = 11 I1'111111] I IIII11
lO 0 lO lO\"
Lifetime (s) Lifetime (s)
Local Noon, Mid-latitude at Equinox. No heterogeneous Bromine reactions
The reaction BrO + HO2 --) HBr + O3 is not included
Figure 2. The calculated midlatitude photochemical lifetimes of reactive bromine species for local noon at equinox.
Heterogeneous bromine reactions were not included in these calculations. These simulations do not include the
reaction HOe + BrO ) HBr +03.
ever, if the products are Br and NO3, then an important
catalytic destruction of ozone can occur. This catalytic
destruction of ozone will be considered in the next sec-
tion.
BrONO2 is produced by the three-body reaction of
BrO with NO2. Because BrONO2 has a relatively
short lifetime, the BrONO2 concentration responds very
rapidly to any change in NO2, as occurs, for exam-
ple, due to denoxification on surfaces. The rate rec-
ommended for the formation of BrONO2 by DeMote
et al. [1992] is based on kinetic measurements made by
Thorn et al. [1993] and Danis et al. [1990]. These mea-
surements were made at over 260 K and so quite large
temperature extrapolations are involved when consider-
ing lower stratospheric temperatures. It would therefore
be valuable to have further measurement studies of this
reaction at the colder temperatures experienced in the
lower stratosphere.
The companion paper œary et al. [this issue] shows
that the catalytic hydrolysis of BrONO2 on sulfate
aerosols is an important sink of BrONO2 in the lower
stratosphere.
HOBr
In the sunlit atmosphere, HOBr is almost in imme-
diate photo chemical steady state with a lifetime of sev-
eral minutes in the lower stratosphere decreasing to a
few seconds in the upper stratosphere (the solid cir-
cles in the right-hand panel of Figure 2). In the sunlit
lower stratosphere HOBr represents between approxi-
mately 20% and 30% of the total BrOy=total inorganic
bromine (the solid circles in the right-hand panel of Fig-
ure 3). The main source of HOBr is the reaction
BrO + HO2 ) HOBr + 02 (1)
k=6x10_2e+ 500
-- AHf 2os K : -217.7 kJ/Mole
BrO + HO2 > HBr + 03 (lb)
Possible minor channel AHf .os K = -31.8 kJ/Mole
The units of this, and all subsequent rate constants,
are molecules cm -a s -. Recent laboratory measure-
ments of reaction (1) were made by Poulet et al. [1992]
and of reaction (lb) by Mellouki et al. [1994]. The ef-
fect of HBr production by reaction (lb) is considered
below in the subsection on HBr.
As can be seen in the companion paper œary et
al. [this issue], in the troposphere and lower strato-
sphere, the heterogeneous production of HOBr on sul-
fate aerosols can play an important role:
H20 + BrONO2 > HOBr + HNO3 (2)
10\"
40-
-
-
_
30-
_
_
_
20-
_
10\"
- Br - ' - Br2
---*--- BrO ,, BrONO
10 o 10' 102 103
I I tillIll I I IIIIII] I I IIIIIII I I IIIII1[
/
-
ß
100 10' 102 103
- BrONO2 -'- HBr
----- HOBr ,, BrCI
100 102 104
I IIIIIIII IIIIIIIII I IIIIIII I IIIIIIII I IIIIIIll I IIIII111 IIII
- 60
:,. , 40
11111111] I llllllll III = 11 I1'111111] I IIII11
lO 0 lO lO\"
Lifetime (s) Lifetime (s)
Local Noon, Mid-latitude at Equinox. No heterogeneous Bromine reactions
The reaction BrO + HO2 --) HBr + O3 is not included
Figure 2. The calculated midlatitude photochemical lifetimes of reactive bromine species for local noon at equinox.
Heterogeneous bromine reactions were not included in these calculations. These simulations do not include the
reaction HOe + BrO ) HBr +03.
ever, if the products are Br and NO3, then an important
catalytic destruction of ozone can occur. This catalytic
destruction of ozone will be considered in the next sec-
tion.
BrONO2 is produced by the three-body reaction of
BrO with NO2. Because BrONO2 has a relatively
short lifetime, the BrONO2 concentration responds very
rapidly to any change in NO2, as occurs, for exam-
ple, due to denoxification on surfaces. The rate rec-
ommended for the formation of BrONO2 by DeMote
et al. [1992] is based on kinetic measurements made by
Thorn et al. [1993] and Danis et al. [1990]. These mea-
surements were made at over 260 K and so quite large
temperature extrapolations are involved when consider-
ing lower stratospheric temperatures. It would therefore
be valuable to have further measurement studies of this
reaction at the colder temperatures experienced in the
lower stratosphere.
The companion paper œary et al. [this issue] shows
that the catalytic hydrolysis of BrONO2 on sulfate
aerosols is an important sink of BrONO2 in the lower
stratosphere.
HOBr
In the sunlit atmosphere, HOBr is almost in imme-
diate photo chemical steady state with a lifetime of sev-
eral minutes in the lower stratosphere decreasing to a
few seconds in the upper stratosphere (the solid cir-
cles in the right-hand panel of Figure 2). In the sunlit
lower stratosphere HOBr represents between approxi-
mately 20% and 30% of the total BrOy=total inorganic
bromine (the solid circles in the right-hand panel of Fig-
ure 3). The main source of HOBr is the reaction
BrO + HO2 ) HOBr + 02 (1)
k=6x10_2e+ 500
-- AHf 2os K : -217.7 kJ/Mole
BrO + HO2 > HBr + 03 (lb)
Possible minor channel AHf .os K = -31.8 kJ/Mole
The units of this, and all subsequent rate constants,
are molecules cm -a s -. Recent laboratory measure-
ments of reaction (1) were made by Poulet et al. [1992]
and of reaction (lb) by Mellouki et al. [1994]. The ef-
fect of HBr production by reaction (lb) is considered
below in the subsection on HBr.
As can be seen in the companion paper œary et
al. [this issue], in the troposphere and lower strato-
sphere, the heterogeneous production of HOBr on sul-
fate aerosols can play an important role:
H20 + BrONO2 > HOBr + HNO3 (2)
Page 4
1508 LARY: GAS PHASE ATMOSPHERIC BROMINE PHOTOCHEMISTRY
40-
-
-
_
30-
_
_
_
_
20-
_
_
- Br/BrO - -- BqJBrO - BrONOJBrO - -- HBr/BrO
--e-- BrO/BrO BrONO/BrO --e-- HOBr/BrO, ---- BrCl/BrO
10 '4 10 '3 10 ' 10\" 10 0\" 104 103 10 ' 10\" 10 ø
I I
\
\
..\ .,,.. \
.,,. __ ø\ !
-
¾ -
10 '4 10 ' 10 ' 10 ' 1 0 ' 10 '4 10 10 ' 10\" 10 ø
Paitioning Paitioning
Lol Noon, Mid-latitude at Equinox. No heterogenus Bromine reacUons
The reaction B + HO HBr + O is not included
60
-40 m
_
-
- <::
_
-30
_
_
-20
Figure 3. The calculated midlatitude partitioning of reactive bromine species for local noon at equinox.
(see also Fan and Jacob [1992] and Hanson and Ravis-
hankara [1995]). HOBr destruction is due to photolysis
and the reaction with O(3p). The rate constant for the
reaction of HOBr with O(3P) has recently been deter-
mined by Nesbitt et al. [1995].
HOBr + hv > Br + OH (3)
Orlando and Burkholder [1995]
HOBr + O(3P) > OH + BrO (4)
43O
k= 1.4xlO-1øe ß
Below approximately 25 km photolysis is the most
important loss of HOBr, whereas above this altitude the
reaction with O(3P) is the main loss of HOBr [Nesbitt
et al., 1995]. This confirms the findings of Nesbitt et
al. [1995]. The lifetime of HOBr varies from about 15
minutes in the sunlit lower stratosphere to a few seconds
in the upper stratosphere. This is based on calculations
using the HOBr absorption cross section which have
recently been measured for the first time by Orlando
and Burkholder [1995].
BrO
The most abundant bromine species in the sunlit
lower stratosphere is normally BrO, which has a life-
time of a few seconds (the solid circles in the left hand
panel of Figure 2). Typically, at 20 km, approximately
40% of BrOy is in the form of BrO rising to a peak
of about 75% at around 40 km (the solid circles in the
left-hand panel of Figure 3). The main source of BrO
is the reaction
Br + 03 ) BrO + 02 (5)
k=l.7x10_11 e oo T
In the sunlit lower stratosphere the main destruction
of BrO is by photolysis (the peak BrO absorption is at
around 325 nm) and reaction with NO
BrO + hv > Br + O(3P)(6)
DeMote et al. [1992]
BrO + NO > Br + NO. (7)
k=8.7x10 l'e -'ø -
In the upper stratosphere the main loss of BrO is due
to the reaction
BrO + O(3P) > O. + Br (8)
In the lower stratosphere the reaction of BrO with
C10 contributes a few percent to the loss rate of BrO.
Close to the ground the reaction of BrO with HO., men-
40-
-
-
_
30-
_
_
_
_
20-
_
_
- Br/BrO - -- BqJBrO - BrONOJBrO - -- HBr/BrO
--e-- BrO/BrO BrONO/BrO --e-- HOBr/BrO, ---- BrCl/BrO
10 '4 10 '3 10 ' 10\" 10 0\" 104 103 10 ' 10\" 10 ø
I I
\
\
..\ .,,.. \
.,,. __ ø\ !
-
¾ -
10 '4 10 ' 10 ' 10 ' 1 0 ' 10 '4 10 10 ' 10\" 10 ø
Paitioning Paitioning
Lol Noon, Mid-latitude at Equinox. No heterogenus Bromine reacUons
The reaction B + HO HBr + O is not included
60
-40 m
_
-
- <::
_
-30
_
_
-20
Figure 3. The calculated midlatitude partitioning of reactive bromine species for local noon at equinox.
(see also Fan and Jacob [1992] and Hanson and Ravis-
hankara [1995]). HOBr destruction is due to photolysis
and the reaction with O(3p). The rate constant for the
reaction of HOBr with O(3P) has recently been deter-
mined by Nesbitt et al. [1995].
HOBr + hv > Br + OH (3)
Orlando and Burkholder [1995]
HOBr + O(3P) > OH + BrO (4)
43O
k= 1.4xlO-1øe ß
Below approximately 25 km photolysis is the most
important loss of HOBr, whereas above this altitude the
reaction with O(3P) is the main loss of HOBr [Nesbitt
et al., 1995]. This confirms the findings of Nesbitt et
al. [1995]. The lifetime of HOBr varies from about 15
minutes in the sunlit lower stratosphere to a few seconds
in the upper stratosphere. This is based on calculations
using the HOBr absorption cross section which have
recently been measured for the first time by Orlando
and Burkholder [1995].
BrO
The most abundant bromine species in the sunlit
lower stratosphere is normally BrO, which has a life-
time of a few seconds (the solid circles in the left hand
panel of Figure 2). Typically, at 20 km, approximately
40% of BrOy is in the form of BrO rising to a peak
of about 75% at around 40 km (the solid circles in the
left-hand panel of Figure 3). The main source of BrO
is the reaction
Br + 03 ) BrO + 02 (5)
k=l.7x10_11 e oo T
In the sunlit lower stratosphere the main destruction
of BrO is by photolysis (the peak BrO absorption is at
around 325 nm) and reaction with NO
BrO + hv > Br + O(3P)(6)
DeMote et al. [1992]
BrO + NO > Br + NO. (7)
k=8.7x10 l'e -'ø -
In the upper stratosphere the main loss of BrO is due
to the reaction
BrO + O(3P) > O. + Br (8)
In the lower stratosphere the reaction of BrO with
C10 contributes a few percent to the loss rate of BrO.
Close to the ground the reaction of BrO with HO., men-
Page 5
LARY: GAS PHASE ATMOSPHERIC BROMINE PHOTOCHEMISTRY 1509
tioned above, contributes about 10% to the total loss of
BrO, as does the formation of BrONO.. As will be
discussed later, the reaction of BrO with C10 is also
important for catalytic ozone destruction.
HBr
Although HBr is the longest lived BrO reservoir, it
still has a lifetime of only about a day in the sunlit
midlatitude lower stratosphere, decreasing to an hour
in the upper stratosphere (the triangles in the right-
hand panel of Figure 2). The lifetime does increase at
high latitudes during winter where there is less sunlight.
According to our current understanding, generally only
a small percent of BrO in the lower stratosphere is in
the form of HBr (the triangles in the right-hand panel
of Figure 3). However, in the troposphere, HBr is gen-
erally a larger fraction of the total BrO. Typically
between about 10% and 40% of tropospheric BrO can
be in the form of HBr if heterogeneous bromine reac-
tions are not considered and if it is assumed that there
is negligible production of HBr by reaction (ls) above.
However, as will be seen in the companion paper œary
et al. [this issue], if heterogeneous bromine reactions
do occur HBr may be only a very small fraction of the
total BrO present both in the troposphere and lower
stratosphere.
HBr is produced mainly by the reactions
Br + HO HBr + O (9)
590
k=l.4x10-1e-W -
Br + HCHO > HBr + HCO (10)
800
k=1.7x10-e- w-
At around 20 km at equinox in the sunlit lower strato-
sphere reactions (9) and (10) make a significant con-
tribution to HBr production. However, as shall be
seen later, the reaction of Br with HCHO can some-
times become the most important source of HBr in the
lower stratosphere. In the upper stratosphere the im-
portance of reaction (10) decreases and reaction (9) is
the main source of HBr, whereas the main source of HBr
in the model troposphere is reaction (10). In the very
low stratosphere and troposphere the higher aldehydes
probably also play a role in producing HBr.
Below about 50 km, HBr is destroyed mainly by re-
action with OH. Above 50 km the reaction of HBr with
O(3P) also becomes an important loss of HBr.
HBr + OH H20 + Br (11)
k=l.lx10 -l
HBr - O(P) OH + Br (12)
k=6.6x10_2 e o T
The partitioning of reactive bromine is very sensi-
tive to the branching ratio of reaction (1) in the lower
stratosphere. Even a very small yield of HBr will in-
crease the HBr concentration at the expense of HOBr.
To illustrate this, Figure 4 shows that an HBr yield of
only 0.1% would double the HBr concentration at 20 km
and a yield of 1% would give a tenfold increase in HBr
at 20 km. If it were assumed that reaction (lb) had a
yield of 0.1%, then between 60% and 70% of the HBr
produced at around 20 km would be due to reaction
(lb); if the yield is 1% then between 80% and 90% of
the HBr produced at around 20 km is due to reaction
(lb). The partitioning of reactive bromine is affected
by the assumed yield of HBr from reaction (1) up to
about 50 km, above this altitude the effect on the HBr
concentration is relatively small.
Garcia and Solomon [1994] have recently examined
the effect of assuming different branching ratios for re-
action (1). They found that the BrO abundance was
critically dependent on the yield of HBr. Their com-
parison between model calculations and observations
suggests that the yield must be substantially less than
5%.
Laboratory measurements of reaction (1) were made
by Poulet et al. [1992]. They pointed out that HBr
is a possible product of this reaction but stated that
the only product they observed at 298 K was HOBr
suggesting a negligible yield for HBr. They did not pre-
clude the formation of HOBr at the lower temperatures
of the stratosphere. Reaction (lb) is a four-centered
reaction and because of the required reaction geometry
these reactions are generally very slow. An upper limit
on the yield of HBr from reaction (lb) has recently been
determined by Mellouki et al. [1994] by measuring an
upper limit for the reverse reaction. The limits were
measured at 301 K and 441 K and were extrapolated
to low temperatures. They found that the yield of HBr
from reaction (lb) is negligible throughout the strato-
sphere. It is likely that less than 0.01% of reaction (1)
yields HBr as a product.
Since the yield of HBr from reaction (1) would af-
fect the fraction of BrOy in the form of BrO it would
also affect the OC10 concentration, since OC10 is pro-
duced mainly by reaction (15). Increasing the yield of
HBr from reaction (1) from 0% to 1% would reduce
the large nighttime OC10 column by just over 16% at
midlatitudes.
Our current understanding of bromine photochem-
istry suggests that the main sources of HBr are reac-
tions (9) and (10). For all of these reactions both the
reactants are present in the atmosphere in relatively
small concentrations. This is in contrast to HC1, which
is formed mainly by the reaction of C1 with the rela-
tively abundant CS4. The extensive literature review
of Baulch et al. [1981] quotes a rate constant for the
analogous bromine reaction which is very slow at strato-
spheric temperatures
Br + CH4 HBr + CH3 (13)
9180 k=7.8x10-e
A reaction which may play a role in the troposphere
tioned above, contributes about 10% to the total loss of
BrO, as does the formation of BrONO.. As will be
discussed later, the reaction of BrO with C10 is also
important for catalytic ozone destruction.
HBr
Although HBr is the longest lived BrO reservoir, it
still has a lifetime of only about a day in the sunlit
midlatitude lower stratosphere, decreasing to an hour
in the upper stratosphere (the triangles in the right-
hand panel of Figure 2). The lifetime does increase at
high latitudes during winter where there is less sunlight.
According to our current understanding, generally only
a small percent of BrO in the lower stratosphere is in
the form of HBr (the triangles in the right-hand panel
of Figure 3). However, in the troposphere, HBr is gen-
erally a larger fraction of the total BrO. Typically
between about 10% and 40% of tropospheric BrO can
be in the form of HBr if heterogeneous bromine reac-
tions are not considered and if it is assumed that there
is negligible production of HBr by reaction (ls) above.
However, as will be seen in the companion paper œary
et al. [this issue], if heterogeneous bromine reactions
do occur HBr may be only a very small fraction of the
total BrO present both in the troposphere and lower
stratosphere.
HBr is produced mainly by the reactions
Br + HO HBr + O (9)
590
k=l.4x10-1e-W -
Br + HCHO > HBr + HCO (10)
800
k=1.7x10-e- w-
At around 20 km at equinox in the sunlit lower strato-
sphere reactions (9) and (10) make a significant con-
tribution to HBr production. However, as shall be
seen later, the reaction of Br with HCHO can some-
times become the most important source of HBr in the
lower stratosphere. In the upper stratosphere the im-
portance of reaction (10) decreases and reaction (9) is
the main source of HBr, whereas the main source of HBr
in the model troposphere is reaction (10). In the very
low stratosphere and troposphere the higher aldehydes
probably also play a role in producing HBr.
Below about 50 km, HBr is destroyed mainly by re-
action with OH. Above 50 km the reaction of HBr with
O(3P) also becomes an important loss of HBr.
HBr + OH H20 + Br (11)
k=l.lx10 -l
HBr - O(P) OH + Br (12)
k=6.6x10_2 e o T
The partitioning of reactive bromine is very sensi-
tive to the branching ratio of reaction (1) in the lower
stratosphere. Even a very small yield of HBr will in-
crease the HBr concentration at the expense of HOBr.
To illustrate this, Figure 4 shows that an HBr yield of
only 0.1% would double the HBr concentration at 20 km
and a yield of 1% would give a tenfold increase in HBr
at 20 km. If it were assumed that reaction (lb) had a
yield of 0.1%, then between 60% and 70% of the HBr
produced at around 20 km would be due to reaction
(lb); if the yield is 1% then between 80% and 90% of
the HBr produced at around 20 km is due to reaction
(lb). The partitioning of reactive bromine is affected
by the assumed yield of HBr from reaction (1) up to
about 50 km, above this altitude the effect on the HBr
concentration is relatively small.
Garcia and Solomon [1994] have recently examined
the effect of assuming different branching ratios for re-
action (1). They found that the BrO abundance was
critically dependent on the yield of HBr. Their com-
parison between model calculations and observations
suggests that the yield must be substantially less than
5%.
Laboratory measurements of reaction (1) were made
by Poulet et al. [1992]. They pointed out that HBr
is a possible product of this reaction but stated that
the only product they observed at 298 K was HOBr
suggesting a negligible yield for HBr. They did not pre-
clude the formation of HOBr at the lower temperatures
of the stratosphere. Reaction (lb) is a four-centered
reaction and because of the required reaction geometry
these reactions are generally very slow. An upper limit
on the yield of HBr from reaction (lb) has recently been
determined by Mellouki et al. [1994] by measuring an
upper limit for the reverse reaction. The limits were
measured at 301 K and 441 K and were extrapolated
to low temperatures. They found that the yield of HBr
from reaction (lb) is negligible throughout the strato-
sphere. It is likely that less than 0.01% of reaction (1)
yields HBr as a product.
Since the yield of HBr from reaction (1) would af-
fect the fraction of BrOy in the form of BrO it would
also affect the OC10 concentration, since OC10 is pro-
duced mainly by reaction (15). Increasing the yield of
HBr from reaction (1) from 0% to 1% would reduce
the large nighttime OC10 column by just over 16% at
midlatitudes.
Our current understanding of bromine photochem-
istry suggests that the main sources of HBr are reac-
tions (9) and (10). For all of these reactions both the
reactants are present in the atmosphere in relatively
small concentrations. This is in contrast to HC1, which
is formed mainly by the reaction of C1 with the rela-
tively abundant CS4. The extensive literature review
of Baulch et al. [1981] quotes a rate constant for the
analogous bromine reaction which is very slow at strato-
spheric temperatures
Br + CH4 HBr + CH3 (13)
9180 k=7.8x10-e
A reaction which may play a role in the troposphere
Page 6
1510 LARY: GAS PHASE ATMOSPHERIC BROMINE PHOTOCHEMISTRY
Yield of HBr
0% ........... 0.1% 1%
0.0 0.1 0.2 0.3 0.4 0.5 0.03 0.06 0.1 0.3 0.6 1.0
70 I I i ; I I ; I I . I I I I I I 70
,,
30 ! 30
', \ \\
', \ ,,
//
20 20
0.0 0.1 0.2 0.3 0.4 0.5 0.03 0. 0.1 0.3 0.6 1.0
HBdBrO, HBr (pptv)
Figure 4. The calculated midlatitude concentration and fraction of BrOy present as HBr for local noon at equinox
if 0%, 0. 1% and 1% of the reaction of HO2 with BrO yields HBr. Heterogeneous bromine reactions were not
included in these calculations.
and lower stratosphere is
Br + H202 . > HBr
k< 5110 -x6
+ HO. (14)
There have been five different studies of reaction (14)
by Leu [1980], Posey et al. [1981], Heneghan and Ben-
son [19831, Toohey et al. [1987] and Mellouki eta!.
[1994]. Apart from Heneghan and Benson [1983] all
show that Br has a very low reactivity towards H202.
Mellouki et al. [1994] suggest that this discrepancy may
have been due to some reactive impurity from the mi-
crowave discharge source used by Heneghan and Benson
[1983].
Mel!ouki et al. [1994] also considered the loss of HBr
due to its reaction with HO2. They concluded that
there was no measurable evidence for this reaction. If
there is an additional source of HBr which could proceed
at a rate comparable to reaction (1), it would consid-
erably affect our understanding of the partitioning of
reactive bromine.
Sr
Br constitutes about 1% of BrOy in the sunlit lower
stratosphere, where it is in photochemical steady state
with a lifetime of about half a second (the solid squares
in the left-hand panel of Figure 2). At 30 km approxi-
mately 10% of BrOy is in the form of Br rising to over
90% above 50 km (the solid squares in the left-hand
panel of Figure 3). This is in contrast to C1, which in
the lower stratosphere typically constitutes only around
0.001% of the total ClOy (-Total inorganic chlorine), in-
creasing to about 4% in the upper stratosphere. As one
descends through the group of halogens from fluorine
through to iodine, the partitioning shifts towards the
more reactive species. Throughout most of the middle
atmosphere the most important loss of Br is reaction
with O3 and the two most important sources of Br are
the photolysis of BrO (reaction (6)) and the reaction of
BrO with NO (reaction (7)). In the upper stratosphere
the reaction of BrO with O(3P) is the most important
source of Br (reaction (8)). Two channels of the reac-
tion of BrO with C10 contribute a few percent to the
production of Br in the sunlit lower stratosphere (re-
actions (15) and (15) below), as does the photolysis of
HOBr and BrONO2.
BrC1
The lifetime of BrC1 in the sunlit lower stratosphere
is approximately a minute (the open squares in the
right-hand panel of Figure 2). During the day BrC1
Yield of HBr
0% ........... 0.1% 1%
0.0 0.1 0.2 0.3 0.4 0.5 0.03 0.06 0.1 0.3 0.6 1.0
70 I I i ; I I ; I I . I I I I I I 70
,,
30 ! 30
', \ \\
', \ ,,
//
20 20
0.0 0.1 0.2 0.3 0.4 0.5 0.03 0. 0.1 0.3 0.6 1.0
HBdBrO, HBr (pptv)
Figure 4. The calculated midlatitude concentration and fraction of BrOy present as HBr for local noon at equinox
if 0%, 0. 1% and 1% of the reaction of HO2 with BrO yields HBr. Heterogeneous bromine reactions were not
included in these calculations.
and lower stratosphere is
Br + H202 . > HBr
k< 5110 -x6
+ HO. (14)
There have been five different studies of reaction (14)
by Leu [1980], Posey et al. [1981], Heneghan and Ben-
son [19831, Toohey et al. [1987] and Mellouki eta!.
[1994]. Apart from Heneghan and Benson [1983] all
show that Br has a very low reactivity towards H202.
Mellouki et al. [1994] suggest that this discrepancy may
have been due to some reactive impurity from the mi-
crowave discharge source used by Heneghan and Benson
[1983].
Mel!ouki et al. [1994] also considered the loss of HBr
due to its reaction with HO2. They concluded that
there was no measurable evidence for this reaction. If
there is an additional source of HBr which could proceed
at a rate comparable to reaction (1), it would consid-
erably affect our understanding of the partitioning of
reactive bromine.
Sr
Br constitutes about 1% of BrOy in the sunlit lower
stratosphere, where it is in photochemical steady state
with a lifetime of about half a second (the solid squares
in the left-hand panel of Figure 2). At 30 km approxi-
mately 10% of BrOy is in the form of Br rising to over
90% above 50 km (the solid squares in the left-hand
panel of Figure 3). This is in contrast to C1, which in
the lower stratosphere typically constitutes only around
0.001% of the total ClOy (-Total inorganic chlorine), in-
creasing to about 4% in the upper stratosphere. As one
descends through the group of halogens from fluorine
through to iodine, the partitioning shifts towards the
more reactive species. Throughout most of the middle
atmosphere the most important loss of Br is reaction
with O3 and the two most important sources of Br are
the photolysis of BrO (reaction (6)) and the reaction of
BrO with NO (reaction (7)). In the upper stratosphere
the reaction of BrO with O(3P) is the most important
source of Br (reaction (8)). Two channels of the reac-
tion of BrO with C10 contribute a few percent to the
production of Br in the sunlit lower stratosphere (re-
actions (15) and (15) below), as does the photolysis of
HOBr and BrONO2.
BrC1
The lifetime of BrC1 in the sunlit lower stratosphere
is approximately a minute (the open squares in the
right-hand panel of Figure 2). During the day BrC1
Page 7
LARY: GAS PHASE ATMOSPHERIC BROM1NE PHOTOCHEMISTRY 1511
generally constitutes much less than 1% of BrOy in
the lower stratosphere (Figure 3) when no heteroge-
neous reactions have occurred on polar stratospheric
clouds (PSCs) for a long time. When PSCs, or cold
sulfate aerosols, are encountered, the BrC1 concentra-
tion rapidly increases and BrC1 can become a sizable
fraction of the total BrOy. BrC1 is typically the ma-
jor nighttime reservoir of BrOy when PSCs are present.
The gas phase production of BrC1 is almost entirely due
to reaction (17):
BrO + C10 ) Br + OC10 (15)
k=l.6x10_ e 430 T
BrO + C10 ) Br + C1OO (16)
k_2.9x10_2 e .o T
BrO + C10 ) BrC1 + O2 (17)
k=5.8x10_x3 e ,o T
The reaction of BrO with C10 is an important reac-
tion as it is the first step in the catalytic loss of ozone
due to the cycle described in the next section. The
loss of BrC1 below about 30 km is almost entirely due
to photolysis, the peak BrC1 absorption is at around
375 nm ($eery and Britton [1964], R. A. Uox, private
communication [1993]). Above about 30 km the main
loss of BrC1 is due to the reaction with O(3P) . This
reaction is not normally included in numerical models
but its rate was determined by Ulyne et al. [1976].
BrC1 d- hv ---+ Br d- C1 (18)
$eery and Britton [1964]
BrC1 + O(3P) --+ BrO -k C1 (19)
k=2.2xl0 -l
Catalytic Cycles
There are several important chain reactions involving
atmospheric bromine species. These chains can propa-
gate after an initiation step transforming reactants into
products by repeated cycles of the chain. The length of
these cycles is limited by termination steps which de-
stroy the chain centre, or radical, involved in the cycle.
The chain length is a measure of how many times the
cycle is executed before the chain centre is removed.
The chain length, Af, is usually defined as the rate of
propagation (th rate of the rate-limiting step), krls di-
vided by the rate of production or destruction of the
chain center, kaest.
chain length, Af- krls/kdest (20)
In the atmosphere there are a very large number of
interacting and competing cycles occurring. Therefore,
a more useful definition has been used which defines
the chain length in terms of the destruction ofthe long-
lived source gases, such as CHaBr, instead of in terms of
the production or destruction of a specific chain centre,
such as Br or BrO. Because the chain length is a ratio
of two rates it is dimensionless.
If a particular radical is involved in a catalytic cy-
cle which has a very long chain length, but it is only
present in small concentrations, the effectiveness of the
cycle will be limited. It is therefore useful to define
a new variable, which shall be called the chain effec-
tiveness, as the chain length multiplied by the rate of
the cycle's rate-limiting step. The chain effectiveness
enables a fair comparison to be made of different cat-
alytic cycles involving species which have very different
concentrations.
chain effectiveness, œ - krls Jf (21)
This section considers the chain length and chain ef-
fectiveness of the various atmospheric bromine catalytic
cycles as a function of altitude compared with other cat-
alytic cycles which are of importance in the atmosphere.
Because this paper focuses on the gas phase chemistry
of atmospheric bromine, the situation chosen was noon
for midlatitudes at the equinox.
As was seen earlier, all of the atmospheric bromine
species are relatively short lived. Therefore, the ter-
mination steps of the gas phase bromine cycles which
involve the formation of HBr or BrONO2 are not very
effective since the Br or BrO can easily be liberated
from these species. In fact, BrONO2 is itself involved in
the catalytic heterogeneous destruction of ozone [Lary
et al., this issue], so formation of BrONO2 is not even
the termination of a chain. This is in marked contrast
to the C1/C10 and NO/NO2 catalytic cycles, where
the formation of the reservoirs HC1 and HNO3 is an
effective termination of the chain reactions. Conse-
quently, the bromine chain reactions tend to have longer
chain lengths than their chlorine counterparts. Cat-
alytic ozone loss can be due to several cycles involving
bromine (Figure 5), which will now be considered in
turn.
Figure 5. The bromine gas phase catalytic ozone
destruction cycles.
generally constitutes much less than 1% of BrOy in
the lower stratosphere (Figure 3) when no heteroge-
neous reactions have occurred on polar stratospheric
clouds (PSCs) for a long time. When PSCs, or cold
sulfate aerosols, are encountered, the BrC1 concentra-
tion rapidly increases and BrC1 can become a sizable
fraction of the total BrOy. BrC1 is typically the ma-
jor nighttime reservoir of BrOy when PSCs are present.
The gas phase production of BrC1 is almost entirely due
to reaction (17):
BrO + C10 ) Br + OC10 (15)
k=l.6x10_ e 430 T
BrO + C10 ) Br + C1OO (16)
k_2.9x10_2 e .o T
BrO + C10 ) BrC1 + O2 (17)
k=5.8x10_x3 e ,o T
The reaction of BrO with C10 is an important reac-
tion as it is the first step in the catalytic loss of ozone
due to the cycle described in the next section. The
loss of BrC1 below about 30 km is almost entirely due
to photolysis, the peak BrC1 absorption is at around
375 nm ($eery and Britton [1964], R. A. Uox, private
communication [1993]). Above about 30 km the main
loss of BrC1 is due to the reaction with O(3P) . This
reaction is not normally included in numerical models
but its rate was determined by Ulyne et al. [1976].
BrC1 d- hv ---+ Br d- C1 (18)
$eery and Britton [1964]
BrC1 + O(3P) --+ BrO -k C1 (19)
k=2.2xl0 -l
Catalytic Cycles
There are several important chain reactions involving
atmospheric bromine species. These chains can propa-
gate after an initiation step transforming reactants into
products by repeated cycles of the chain. The length of
these cycles is limited by termination steps which de-
stroy the chain centre, or radical, involved in the cycle.
The chain length is a measure of how many times the
cycle is executed before the chain centre is removed.
The chain length, Af, is usually defined as the rate of
propagation (th rate of the rate-limiting step), krls di-
vided by the rate of production or destruction of the
chain center, kaest.
chain length, Af- krls/kdest (20)
In the atmosphere there are a very large number of
interacting and competing cycles occurring. Therefore,
a more useful definition has been used which defines
the chain length in terms of the destruction ofthe long-
lived source gases, such as CHaBr, instead of in terms of
the production or destruction of a specific chain centre,
such as Br or BrO. Because the chain length is a ratio
of two rates it is dimensionless.
If a particular radical is involved in a catalytic cy-
cle which has a very long chain length, but it is only
present in small concentrations, the effectiveness of the
cycle will be limited. It is therefore useful to define
a new variable, which shall be called the chain effec-
tiveness, as the chain length multiplied by the rate of
the cycle's rate-limiting step. The chain effectiveness
enables a fair comparison to be made of different cat-
alytic cycles involving species which have very different
concentrations.
chain effectiveness, œ - krls Jf (21)
This section considers the chain length and chain ef-
fectiveness of the various atmospheric bromine catalytic
cycles as a function of altitude compared with other cat-
alytic cycles which are of importance in the atmosphere.
Because this paper focuses on the gas phase chemistry
of atmospheric bromine, the situation chosen was noon
for midlatitudes at the equinox.
As was seen earlier, all of the atmospheric bromine
species are relatively short lived. Therefore, the ter-
mination steps of the gas phase bromine cycles which
involve the formation of HBr or BrONO2 are not very
effective since the Br or BrO can easily be liberated
from these species. In fact, BrONO2 is itself involved in
the catalytic heterogeneous destruction of ozone [Lary
et al., this issue], so formation of BrONO2 is not even
the termination of a chain. This is in marked contrast
to the C1/C10 and NO/NO2 catalytic cycles, where
the formation of the reservoirs HC1 and HNO3 is an
effective termination of the chain reactions. Conse-
quently, the bromine chain reactions tend to have longer
chain lengths than their chlorine counterparts. Cat-
alytic ozone loss can be due to several cycles involving
bromine (Figure 5), which will now be considered in
turn.
Figure 5. The bromine gas phase catalytic ozone
destruction cycles.
Page 8
1512 LARY: GAS PHASE ATMOSPHERIC BROMINE PHOTOCHEMISTRY
o NO/NO
10 '2 10 0 102 104
10 '2 10 0 10 2 10 4
Chain Length
010/HO2 [] BrO/HO2
10 10 0 105 10 ø
10 10 0 105 10 ø
Chain Effectiveness
Local Noon, Mid-latitude at Equinox.
E
4o ß
_
_
-30
_
_
_
_
-20
_
-
_
30-
_
I i I
10 '2 10 0 10 2 10 4
CIO/NO2 BrO/NO2 []
10 '2 10 0 10 2 10 4
Chain Length
BrO/010 (A) - BrO/010 (B)
10 10 0 105
10 100 105
Chain Effectiveness
--
..
_
_
-30
_
_
_
_
-20
_
Local Noon, Mid-latitude at Equinox.
Figure 6. The calculated midlatitude chain length and chain effectiveness of various catalytic cycles for local noon
at equinox. The chain effectiveness i the chain length multiplied by the rate of the cycle's rate-limiting step and
has units of molecules cm -s s -[.
o NO/NO
10 '2 10 0 102 104
10 '2 10 0 10 2 10 4
Chain Length
010/HO2 [] BrO/HO2
10 10 0 105 10 ø
10 10 0 105 10 ø
Chain Effectiveness
Local Noon, Mid-latitude at Equinox.
E
4o ß
_
_
-30
_
_
_
_
-20
_
-
_
30-
_
I i I
10 '2 10 0 10 2 10 4
CIO/NO2 BrO/NO2 []
10 '2 10 0 10 2 10 4
Chain Length
BrO/010 (A) - BrO/010 (B)
10 10 0 105
10 100 105
Chain Effectiveness
--
..
_
_
-30
_
_
_
_
-20
_
Local Noon, Mid-latitude at Equinox.
Figure 6. The calculated midlatitude chain length and chain effectiveness of various catalytic cycles for local noon
at equinox. The chain effectiveness i the chain length multiplied by the rate of the cycle's rate-limiting step and
has units of molecules cm -s s -[.
Page 9
LARY: GAS PHASE ATMOSPHERIC BROMINE PHOTOCHEMISTRY 1513
BrO/C10
In polar regions the coupling of BrO and C10 chem-
istry via the BrO/C10 catalytic cycle is particularly
important. The coupling is also important at midlati-
tudes. The BrO/C10 cycle can operate via two routes.
One route, here referred to as route A, results in the
formation of BrCh
BrO + C10 BrC1 + O.
BrC1 + h Br + C1
Br + 03 BrO + O2
C1 + O C10 + O.
Net 203 302
Depending on the physical conditions, in the low
stratosphere below about 15 km the rate-limiting step
is the formation of BrC1. However, higher up in the
stratosphere it is the photolysis of BrC1.
In the sunlit stratosphere between 15 and 35 km this
cycle has a chain length of approximately 103 with the
chain length decreasing above 35 km (Figure 6). The
chain effectiveness of this cycle is approximately 106
molecules cm -3 s -x between about 17 and 30 km (Fig-
ure 6). This can be compared to the NO/NO2 cat-
alytic cycle [Crutzen, 1970; Johnston, 1971], which is
the most important ozone loss cycle at 38 km where it
has a chain length of 10 4 and a chain effectiveness of
approximately 101ø molecules cm -3 s -, decreasing to
106 molecules cm -3 s - at 17 km and 102 molecules
cm -3 s -1 at 10 km (Figure 6).
The alternative cycle, here referred to as route B, is
much more effective than route A and involves the for-
marion of C1OO:
BrO + C10 Br + C1OO
C1OO M) C1 -]- 02
Br + O3 BrO + O2
C1 + O3 C10 + O2
Net 203 30.
The rate-limiting step is the formation of C1OO.
Throughout the sunlit lower stratosphere this cycle has
a chain length of approximately 104 (Figure 6). The
chain effectiveness of this cycle is approximately 10 s
molecules cm -3 s - between about 20 and 30 km (Fig-
ure 6). Route B of the C10/BrO catalytic cycle is ap-
proximately an order of magnitude more effective at de-
stroying ozone between 16 and 20 km than the NO/NO2
catalytic cycle.
The efficiency of the BrO/C10 cycle is reduced by
the alternate channel of the BrO + C10 reaction which
yields OC10 (reaction (15)). OC10 is photolyzed to give
an oxygen atom, this channel constitutes a null cycle.
BrO/HO.
The BrO/HO. catalytic cycle involves the formation
of HOBr.
HO2 + BrO HOBr + 02
HOBr + h OH + Br
Br + O3 BrO + 02
OH + Os HO2 + 02
Net 203 30.
Below about 15 km the rate-limiting step is the pho-
tolysis of HOBr; above this the formation of HOBr is
the rate limiting step. In the sunlit lower stratosphere
this cycle has a long chain length of approximately 103
(Figure 6). The chain effectiveness of the BrO/HO2
catalytic cycle is greater than 106 molecules cm -3 s -
between 13 and 30 kin. The chain length and effective-
ness decrease above 35 km. The BrO/HO. catalytic
cycle is approximately 2 orders of magnitude more ef-
fective at destroying ozone at 12 km than the NO/NO.
catalytic cycle, and twice as effective at 20 km.
The analogous C10/HO. catalytic cycle has a much
shorter chain length of less than 50 above 15 km, where
the rate-limiting step is the photolysis of HOC1 (Fig-
ure 6). The C10/HO. chain length is approximately 10'
close to the tropopause and in the troposphere, where
the rate-limiting step is the reaction of OH with 03.
Between 15 and 20 km the BrO/HO2 cycle is between
i and 2 orders of magnitude more effective than the
C10/HO2 cycle at destroying ozone, even though BrO
is much less abundant than C10. This finding empha-
sizes the importance of atmospheric bromine for cat-
alytic ozone destruction.
Br/BrO
The Br/BrO catalytic cycle increases in length from
102 in the lower stratosphere to 104 in the upper strato-
sphere (Figure 6).
Br - O3 BrO - O.
BrO + O(sp) Br + O2
O3 + O(SP) 202
At all sunlit altitudes the reaction of BrO with O(sP)
is the rate limiting step. The chain effectiveness in-
creases from 103 molecules cm -3 s -1 at 12 km to 10 ø
molecules cm -3 s -1 at 38 km (Figure 7). The analo-
gous C1/C10 has a shorter chain length, which increases
from 10 in the lower stratosphere to l03 in the up-
per stratosphere and has a chain effectiveness which
increases from 102 molecules cm -3 s - at 12 km to
10 ø molecules cm -3 s -1 at 38 kin. Consequently at
38 km the NO/NO2 cycle is the main ozone loss cycle
but above this the C1/C10 cycle is the main ozone loss
cycle [$tolarski and Cicerone, 1974; Molina and Row-
land, 1974].
BrO/NO2
As was recently pointed out by Burkholder et al.
[1995], if the products of BrONO2 photolysis are Br
and NOs, then a very effective BrONO2 catalytic cycle
can exist, namely
BrO/C10
In polar regions the coupling of BrO and C10 chem-
istry via the BrO/C10 catalytic cycle is particularly
important. The coupling is also important at midlati-
tudes. The BrO/C10 cycle can operate via two routes.
One route, here referred to as route A, results in the
formation of BrCh
BrO + C10 BrC1 + O.
BrC1 + h Br + C1
Br + 03 BrO + O2
C1 + O C10 + O.
Net 203 302
Depending on the physical conditions, in the low
stratosphere below about 15 km the rate-limiting step
is the formation of BrC1. However, higher up in the
stratosphere it is the photolysis of BrC1.
In the sunlit stratosphere between 15 and 35 km this
cycle has a chain length of approximately 103 with the
chain length decreasing above 35 km (Figure 6). The
chain effectiveness of this cycle is approximately 106
molecules cm -3 s -x between about 17 and 30 km (Fig-
ure 6). This can be compared to the NO/NO2 cat-
alytic cycle [Crutzen, 1970; Johnston, 1971], which is
the most important ozone loss cycle at 38 km where it
has a chain length of 10 4 and a chain effectiveness of
approximately 101ø molecules cm -3 s -, decreasing to
106 molecules cm -3 s - at 17 km and 102 molecules
cm -3 s -1 at 10 km (Figure 6).
The alternative cycle, here referred to as route B, is
much more effective than route A and involves the for-
marion of C1OO:
BrO + C10 Br + C1OO
C1OO M) C1 -]- 02
Br + O3 BrO + O2
C1 + O3 C10 + O2
Net 203 30.
The rate-limiting step is the formation of C1OO.
Throughout the sunlit lower stratosphere this cycle has
a chain length of approximately 104 (Figure 6). The
chain effectiveness of this cycle is approximately 10 s
molecules cm -3 s - between about 20 and 30 km (Fig-
ure 6). Route B of the C10/BrO catalytic cycle is ap-
proximately an order of magnitude more effective at de-
stroying ozone between 16 and 20 km than the NO/NO2
catalytic cycle.
The efficiency of the BrO/C10 cycle is reduced by
the alternate channel of the BrO + C10 reaction which
yields OC10 (reaction (15)). OC10 is photolyzed to give
an oxygen atom, this channel constitutes a null cycle.
BrO/HO.
The BrO/HO. catalytic cycle involves the formation
of HOBr.
HO2 + BrO HOBr + 02
HOBr + h OH + Br
Br + O3 BrO + 02
OH + Os HO2 + 02
Net 203 30.
Below about 15 km the rate-limiting step is the pho-
tolysis of HOBr; above this the formation of HOBr is
the rate limiting step. In the sunlit lower stratosphere
this cycle has a long chain length of approximately 103
(Figure 6). The chain effectiveness of the BrO/HO2
catalytic cycle is greater than 106 molecules cm -3 s -
between 13 and 30 kin. The chain length and effective-
ness decrease above 35 km. The BrO/HO. catalytic
cycle is approximately 2 orders of magnitude more ef-
fective at destroying ozone at 12 km than the NO/NO.
catalytic cycle, and twice as effective at 20 km.
The analogous C10/HO. catalytic cycle has a much
shorter chain length of less than 50 above 15 km, where
the rate-limiting step is the photolysis of HOC1 (Fig-
ure 6). The C10/HO. chain length is approximately 10'
close to the tropopause and in the troposphere, where
the rate-limiting step is the reaction of OH with 03.
Between 15 and 20 km the BrO/HO2 cycle is between
i and 2 orders of magnitude more effective than the
C10/HO2 cycle at destroying ozone, even though BrO
is much less abundant than C10. This finding empha-
sizes the importance of atmospheric bromine for cat-
alytic ozone destruction.
Br/BrO
The Br/BrO catalytic cycle increases in length from
102 in the lower stratosphere to 104 in the upper strato-
sphere (Figure 6).
Br - O3 BrO - O.
BrO + O(sp) Br + O2
O3 + O(SP) 202
At all sunlit altitudes the reaction of BrO with O(sP)
is the rate limiting step. The chain effectiveness in-
creases from 103 molecules cm -3 s -1 at 12 km to 10 ø
molecules cm -3 s -1 at 38 km (Figure 7). The analo-
gous C1/C10 has a shorter chain length, which increases
from 10 in the lower stratosphere to l03 in the up-
per stratosphere and has a chain effectiveness which
increases from 102 molecules cm -3 s - at 12 km to
10 ø molecules cm -3 s -1 at 38 kin. Consequently at
38 km the NO/NO2 cycle is the main ozone loss cycle
but above this the C1/C10 cycle is the main ozone loss
cycle [$tolarski and Cicerone, 1974; Molina and Row-
land, 1974].
BrO/NO2
As was recently pointed out by Burkholder et al.
[1995], if the products of BrONO2 photolysis are Br
and NOs, then a very effective BrONO2 catalytic cycle
can exist, namely
Page 10
1514 LARY: GAS PHASE ATMOSPHERIC BROMINE PHOTOCHEMISTRY
o CI/CIO Br/BrO [] OH/HO
10 100 10 10 10 100 10 10 10 10 10 ø
I i i
I I I I I I I I I I I
10 ' 10 0 10 = 10 4 10a10 ø 10 = 10 4 10 a 10 a 10 ø
Chain Length Chain Effectiveness
Local Noon, Mid-latitude at Equinox.
Figure 7. The calculated midlatitude chain length and chain effectiveness of various catalytic cycles for local noon
at equinox.
BrO + NO2 M> BrONO2
BrONO2 + h > Br + NO3
NO3 -I- hz > NO + 02
NO + 03 > NO2 + 02
Br + O ) BrO + O2
Net 203 > 302
Depending on the conditions, the rate-limiting step of
the cycle is the photolysis of BrONO2 or of NO3 to NO.
If it is assumed that the main BrONO2 photolysis prod-
ucts are Br and NOs then the BrO/NO2 cycle between
about 15 km and 30 km has a chain length of more than
103. The chain length decreases above 30 km. The
chain effectiveness i approximately 107 molecules cm -3
s -x between about 15 and 30 km (Figure 6). This re-
sult can be compared to the analolgous C10/NO2 cy-
cle [Toumi et al., 1993] which has a chain length of
about 102 at the tropopause decreasing to only 3 at
40 km, and a chain effectiveness of 105 molecules cm -3
s -x close to the tropopause decreasing to 102 molecules
cm -3 s -1 at 38 km. This finding emphasizes the point
made by Toumi et aL [1993] that the C10/NO2 cycle
is only important for high levels of C1ONO2. For typi-
cal levels of BrONO2 and C1ONO2 the BrO/NO2 cycle
is more effective at removing ozone than the analogous
C10/NO2 cycle.
Summary
The current knowledge of gas phase bromine chem-
istry has been reviewed and two gas phase reactions
not normally considered have been found to be impor-
tant in the upper stratosphere. They are the reactions
of O(3P) with BrC1 and HOBr whose rates were mea-
sured by Clyne et al. [1976] and Nesbitt et al. [1995],
respectively.
The effectiveness of the ozone catalytic loss cycles
involving bromine has been quantified by considering
their chain length and effectiveness. The chain effec-
tiveness is a new variable defined as the chain length
multiplied by the rate of the cycle's rate-limiting step.
The chain effectiveness enables a fair comparison of dif-
ferent catalytic cycles involving species which have very
different concentrations.
It is shown that in the low stratosphere the most ef-
fective ozone loss cycles are the BrO/HO2 and BrO/C10
cycles. Both catalytic cycles have long chain lengths of
greater than 103 and a chain effectiveness of between
106 and 108 molecules cm -3 s -1 in the lower strato-
sphere. The cycles are therefore effective ozone destruc-
tion cycles even when no PSCs are present.
If it is assumed that the main photolysis products
of BrONO2 are Br and NO3, then the BrO/NO2 cycle
between about 15 km and 30 km has a chain length of
at least 103. The chain length decreases above 30 km.
This cycle will only be effective for ozone loss if BrONO2
photolysis leads to the production of Br and NO3. This
conclusion agrees with the recent findings of Burkholder
et al. [1995] and can be compared to the anolgous
C10/NO2 cycle [Toumi et al., 1993], which has a chain
length of about 102 at the tropopause decreasing toonly
3 at 40 km.
o CI/CIO Br/BrO [] OH/HO
10 100 10 10 10 100 10 10 10 10 10 ø
I i i
I I I I I I I I I I I
10 ' 10 0 10 = 10 4 10a10 ø 10 = 10 4 10 a 10 a 10 ø
Chain Length Chain Effectiveness
Local Noon, Mid-latitude at Equinox.
Figure 7. The calculated midlatitude chain length and chain effectiveness of various catalytic cycles for local noon
at equinox.
BrO + NO2 M> BrONO2
BrONO2 + h > Br + NO3
NO3 -I- hz > NO + 02
NO + 03 > NO2 + 02
Br + O ) BrO + O2
Net 203 > 302
Depending on the conditions, the rate-limiting step of
the cycle is the photolysis of BrONO2 or of NO3 to NO.
If it is assumed that the main BrONO2 photolysis prod-
ucts are Br and NOs then the BrO/NO2 cycle between
about 15 km and 30 km has a chain length of more than
103. The chain length decreases above 30 km. The
chain effectiveness i approximately 107 molecules cm -3
s -x between about 15 and 30 km (Figure 6). This re-
sult can be compared to the analolgous C10/NO2 cy-
cle [Toumi et al., 1993] which has a chain length of
about 102 at the tropopause decreasing to only 3 at
40 km, and a chain effectiveness of 105 molecules cm -3
s -x close to the tropopause decreasing to 102 molecules
cm -3 s -1 at 38 km. This finding emphasizes the point
made by Toumi et aL [1993] that the C10/NO2 cycle
is only important for high levels of C1ONO2. For typi-
cal levels of BrONO2 and C1ONO2 the BrO/NO2 cycle
is more effective at removing ozone than the analogous
C10/NO2 cycle.
Summary
The current knowledge of gas phase bromine chem-
istry has been reviewed and two gas phase reactions
not normally considered have been found to be impor-
tant in the upper stratosphere. They are the reactions
of O(3P) with BrC1 and HOBr whose rates were mea-
sured by Clyne et al. [1976] and Nesbitt et al. [1995],
respectively.
The effectiveness of the ozone catalytic loss cycles
involving bromine has been quantified by considering
their chain length and effectiveness. The chain effec-
tiveness is a new variable defined as the chain length
multiplied by the rate of the cycle's rate-limiting step.
The chain effectiveness enables a fair comparison of dif-
ferent catalytic cycles involving species which have very
different concentrations.
It is shown that in the low stratosphere the most ef-
fective ozone loss cycles are the BrO/HO2 and BrO/C10
cycles. Both catalytic cycles have long chain lengths of
greater than 103 and a chain effectiveness of between
106 and 108 molecules cm -3 s -1 in the lower strato-
sphere. The cycles are therefore effective ozone destruc-
tion cycles even when no PSCs are present.
If it is assumed that the main photolysis products
of BrONO2 are Br and NO3, then the BrO/NO2 cycle
between about 15 km and 30 km has a chain length of
at least 103. The chain length decreases above 30 km.
This cycle will only be effective for ozone loss if BrONO2
photolysis leads to the production of Br and NO3. This
conclusion agrees with the recent findings of Burkholder
et al. [1995] and can be compared to the anolgous
C10/NO2 cycle [Toumi et al., 1993], which has a chain
length of about 102 at the tropopause decreasing toonly
3 at 40 km.
Page 11
LARY: GAS PHASE ATMOSPHERIC BROMINE PHOTOCHEMISTRY 1515
Acknowledgments. The author wishes to thank R.
A. Cox for very useful conversations and seminars, J. A.
Pyle for his support, J. J. Orlando and J. B. Burkholder for
making their results available to us before publication and
D. Shallcross and J. Sessler for useful conversations. The
Centre for Atmospheric Science is a joint initiative of the
Department of Chemistry and the Department of Applied
Mathematics and Theoretical Physics. This work forms part
of the NERC U.K. Universities Global Atmospheric Mod-
elling Programme.
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Acknowledgments. The author wishes to thank R.
A. Cox for very useful conversations and seminars, J. A.
Pyle for his support, J. J. Orlando and J. B. Burkholder for
making their results available to us before publication and
D. Shallcross and J. Sessler for useful conversations. The
Centre for Atmospheric Science is a joint initiative of the
Department of Chemistry and the Department of Applied
Mathematics and Theoretical Physics. This work forms part
of the NERC U.K. Universities Global Atmospheric Mod-
elling Programme.
References
Anderson, D. E., The troposphere to stratosphere radiation
field at twilight: A spherical model, Planet. Space $ci., 31
(12), 1,517-1,523, 1983.
Atkinson, R., D. L. Baulch, R. A. Cox, R. F. Hampson,
J,A. Kerr and J. Troe, Evaluated kinetic and photochem-
ical data for atmospheric chemistry- Supplement IV, IU-
PAC subcommittee on gas kinetic data evaluation for at-
mospheric chemistry, J. Phys. Chem. Ref. Data, 21 (6),
1,125-1,568, 1992.
Baulch, D. L., J., Duxbury, S. J., Grant and D.C. Mon-
tague, Evaluated kinetic data for high temperature re-
actions. Volume 4 Homogeneous gas phase reactions of
halogen and cyanide containing species, J. Phys. Chem.
Ref. Data, 10, supplement 1,1-1, 1-721, 1981.
Berg, W. W., L. E. Heidt, W. Pollock, P. D. Sperry, R. J.
Cicerone and E. S. Gladhey, Brominated organic species
in the Arctic atmosphere, Geophys. Res. Left., 11, 429-
432, 1984.
Burkholder, J. B., A. R. Ravishankara and S. Solomon,
UV/visible and IR absorption cross sections of BrONO.,
J. Geophys. Res., 100 (D8), 16,793-16,800, 1995.
Cicerone, R. J., L. E. Heidt and W. H. Pollock, Measure-
ments of atmospheric methyl bromide and bromoform, J.
Geophys. Res., 93, 3,745-3,749, 1988.
Clyne, M. A. A., P. B. Monkhouse and L. W. Townsend,
Reactions of O(3P) atoms with halogens: The rate con-
stants for the elementary reactions O(3P) + BrC1, O(3P)
+ Br2 and O(3P) + CI., Int. J. Chem. Kinet., 8, 425,
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the Arctic and Arctic haze, Geophys. Res. Lett., 11 (5),
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Kinet., œ5 (7), 521-537, 1993.
Toohey, D. W., W. H. Brune and J. G. Anderson, Mecha-
nism and kinetics of Br + HO2 -+ HBr + O. and Br +
H.O. -+ products over the temperature range 260-390 K,
J. Phys. Chem., 91, 1,215-1,222, 1987.
Toumi, R., R. L. Jones and J. A. Pyle, Stratospheric ozone
depletion by C1ONO2 photolysis, Nature, 365, 37-39,
1993.
Yung, Y. L., J.P., Pinto, R. T., Watson and S. P. Sander,
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lower stratosphere, J. Atmos. $ci., 37, 339-353, 1980.
World Meteorological Organisation, Scientific assessment of
stratospheric ozone: 1988, WMO Global Ozone Research
and Monitoring Project, Rep. œ0, 1990.
World Meteorological Organisation, Scientific assessment of
stratospheric ozone: 1991, WMO Global Ozone Research
and Monitoring Project, Rep. œ5, 1992.
D. J. Lary, Centre for Atmospheric Science, Department
of Chemistry, Cambridge University, Lensfield Road, Cam-
bridge, CB2 1EW, U.K. (email:david@atm.cm.cam.ac.uk)
(Received March 9, 1995; revised June 29, 1995;
accepted June 29, 1995.)
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