Journal ofAtmospheric Chemistry 13: 373-392, 1991.
0 1991 Kluwer Academic Publishers. Printed in the Netherlands.
373
Diffuse Radiative, bought, and
Photochemistry - I
D. J. LARY and J. A. PYLE
Department of Chemishy, University of Cambridge, Cambridge CB2 1EU: U.K.
(Received: 9 July 1991)
Abstract. A photochemi~al scheme which includes a detailed treatment of multiple scattering up to
soiar zenith angles of 96” (developed for use in a GCM) has been used to study partitioning within
chemical families. Attention is drawn to the different zenith angle dependence of diffuse radiation for
the two spectral regions d < 310 nm and I > 310 nm. The effect that this has on the so-called 40 km
ozone problem is discussed. The importance of correctly including multiple scattering for polar ozone
studies is emphasised.
Key words: multiple scattering, ozone problem, polar ozone.
1. Introduction
Radiation incident on the atmosphere embodies the ultimate driving force for all
the atmospheric processes which occur. The major difficulty in computing the solar
radiation field is a correct description of multiple scattering. Goody (1964) points
out that the diffuse flux is often neglected ‘for reasons which are rarely stated ex-
plicitly, but which may well represent a desire to avoid a particularly difficult
problem’. This study uses an accurate and computationally efficient method for cal-
culating the effects of multiple scattering for solar zenith angles up to 96” (Meier et
al., 1982; Anderson, 1983; Lary, 1991).
Just over a decade ago, considerable effort was expended on including the
effects of diffuse radiation in photochemical models, beginning with the work of
Luther and Gelinas (1976) and followed by other studies such as Fiocco (1979)
and ~ugnai et al. (1979). That early work hi~lighted the effects of the diffuse
radiation field, particularly for 12 > 310 nm. However, with the improvement of
photochemical data over recent years, and the use of a more detailed radiative
transfer model, this study illustrates the significant role which is also played by the
diffuse radiation field for I < 310 nm. For example, it is shown that in addition to
the use of accurte temperature profiles, a correct treatment of the diffuse radiative
field is aIso important in the modelling of ozone above 35 km, a matter of major
concern over recent years (for example, $8.7 WMO, 1986; $3.1 WMO, 1990).
The solar zenith angle dependence of the atmospheric radiation field changes
with wavelength. A transition occurs at approximately 310 nm. For 1 < 310 nm
atmospheric absorption is strong and the cont~bution of the diffuse flux to the total

374 D. J. LARY AND J. A. PYLE
radiation field increases rapidly with increasing solar zenith angles. Conversely, for
a > 310 nm atmospheric absorption is weak and the contribution of the diffuse flux
to the total radiation field decreases with increasing solar zenith angles.
The wavelength region 175 nm < A < 320 nm plays a major part in stratospheric
photochemistry. Very little radiation of ;1 < 310 nm reaches the earth’s surface due
to the strong absorption by molecular oxygen for ;1< 242 nm and by ozone for
d < 310 nm. Consequently, under normal conditions (i.e. no severe ozone deple-
tion), the ground albedo has little effect on the radiation field for Iz < 310 nm.
However for 1> 310 nm, radiation experiences relatively little atmospheric
absorption, and so can reach the lower atmosphere where a significant amount of
molecular scattering takes place. As a result, the ground reflection of both the
direct and the diffuse radiation can play a major role in determining the photolysis
which occurs for )3 > 310 nm (Meier eta/., 1982; Nicolet et aI., 1982).
It is important to realise that although the total number density of molecules in
the middle atmosphere is significantly lower than in the troposphere, the molecular
scattering which does occur is a strong function of the wavelength (proportional to
A-“). Therefore the diffuse radiation fietd at short wavelengths must not be ignored
in photochemical models, even if there are only a small number of scatterers in the
stratosphere. In fact, many remote sensing techniques directly use the diffuse ultra-
violet radiation field (e.g. SBUV, Solar Backscattered UltraViolet). Moreover,
various measurements have emphasised the importance of the diffuse radiation
field for A < 310 nm (e.g. the measurements at 40 km by Herman and Mental1
(1982)). Some photochemical models have not included the effects of multiple
scattering for A < 310 nm (see, e.g., the various two-dimensional models inter-
compared in Jackman et al. (1988). This omission has far reaching implications
since photolysis at i < 310 nm controls the concentration of many constituents
which are of vital importance, particularly 0( ID). However, many models currently
in use do include the simplified two-stream treatment of multiple scattering. This
method is good for solar zenith angles less than 80”.
This paper describes the use of a detailed radiative transfer model, developed
for use within middle atmosphere photochemical schemes. These schemes are now
being used extensively in a number of atmospheric models being developed at the
University of Cambridge. In this paper the general features of the scheme are
described, concentrating, in particular, on characterising the general response of
the photoche~~al scheme to the inclusion of diffuse radiation. In a companion
paper, the model will be compared with a variety of measurements. These compari-
sons provide, firstly, validation of the model and secondly, demonstrate that the
model is capable of explaining a number of interesting, previously unexplained,
features of these measurements.
Sections 1 and 2 of this paper briefly describe the radiative transfer and photo-
chemical schemes. Section 3 analyses the effects of diffuse radiation on the parti-
tioning of stratospheric constituents by comparing a model which includes a treat-
ment of multiple scattering to one which does not. Section 4 considers the role of

DIFFUSE RADIATION, TWILIGHT. AND PHOTOCHEMISTRY - I 375
diffuse radiation in relation to the so-called 40 km ozone problem. Section 5
demonstrates briefly the importance of including multiple scattering for solar
zenith angles greater than 90” in model studies of polar ozone.
2. Photochemical Radiative Transfer Model
The model used in this study is a new implementation of the scheme described by
Meier et al. (1982). It has been extended after Anderson (1983) to describe
correctly the radiation field for solar zenith angles greater than 75”. The radiation
into any volume element of the model atmosphere has four contributions: (A) The
direct solar flux, (B) the diffuse flux incident from all directions, (C) the ground
reflection of the direct solar flux and (D) the ground reflection of the diffuse flux.
This is illustrated schematically in Figure 1.
The radiation field is calculated by solving the integral equation of radiative
transfer. The model is then used to calculate the normalised source function, S.
This is the number by which the solar flux incident at the top of the atmosphere
must be multiplied by to yield the radiation field at a given point. The detailed
mathematical description of these four contributions is described by Meier et al.
(I 982) and Lary (1991). The direct flux is treated using a full spherical geometry,
and the scattered flux is treated using the plane parallel approximation. Using the
plane parallel approximation to describe the multiple scattering, results in an
underestimate of the radiation field for solar zenith angles greater than 93”. We
have usually carried calculations upto 96”, with some loss of accuracy at the largest
angles. The accuracy of this method has been demonstrated by Anderson (1983)
and by the good agreement with several measurement studies presented by Lary
(1991) and in the companion paper Lary and Pyle (1991). The studies presented in
this paper assume clear sky conditions.
Photolysis rates are calculated by making use of an enhancement factor, S,
Fig. 1. Schematic diagram of the radiative transfer model used in this study (adapted from Meier et
d(1982)).

376 D. J. LARY AND J. A. PYLE
(Meier et al., 1982), which is defined as the total flux, F,, integrated over all direct-
tions, which is available for photolysis at any given point in the atmosphere
normalised by the solar flux incident at the top of the atmosphere, F,,,
0)
Any photolysis rate j, can readily be calculated from a knowledge of the solar flux
incident at the top of the atmosphere Fol, the absorption cross section, a,, the
quantum efficiency, h, and the enhancement factor, S,, using
Ak x, Aground > = l b&k x, Agrouncd h~n;dl. (2)
Note that the enhancement factor S, is a function of wavelength Iz, solar zenith
angle x, altitude z, and ground albedo Aground. S, also depends on the ozone, tem-
perature and aerosol profiles which are used. In this study atmospheric aerosols
have not been included.
3. Stratospheric Photochemical Scheme
Seventy-nine chemical and photochemical reactions are used to describe the
stratospheric chemistry of O,, NO,, HO,, and ClO, (Table I). A more detailed
description of the model is given in Lary (1991). The kinetic data were taken from
DeMore et al. (1990) apart from the following: the absorption cross section for the
Herzberg continuum of molecular oxygen was taken from Nicolet and Kennes
(1986), and WMO (1986); the absorption cross-section for the Schumann-Runge
bands of molecular oxygen are calculated using the parameterisation of Frederick
(1985); the temperature dependence of the 0, absorption cross section in the
spectral region 264 nm < il < 345 nm is calculated using a quadratic fit to the data
set of A. M. Bass presented by Frederick (1985); the absorption cross sections of
NO in the 6(0-O) and 6(1-O) bands are calculated using the parameterisation of
Allen and Frederick (1982). This parameterisation applies for the region above 20
km, and for solar zenith angles up to 85”. Outside this domain, the parameterisa-
tion does not apply, and the absorption cross section is set to zero. The tempera-
ture dependent absorption cross sections of the halocarbons CH,Cl, Ccl,,
Fll(CF,Cl& and F22(CHF,Cl) are calculated using the parameterisations of
Simon et al. (1988).
4. Diffuse Radiation and the Partitioning of Stratospheric Constituents
The paragraphs that follow consider the effect of diffuse radiation on the parti-
tioning of oxygen, nitrogen, chlorine and hydrogen constituents, with particular
emphasis placed on odd oxygen.

)IFFUSE RADIATION, TWILIGHT, AND PHOTOCHEMISTRY - I 377
Table I. Reactions considered
0
0
W’D)
O(‘D)
O(‘D)
OH
02
HO,
OH
H
OH
OH
NO,
NO
NO,
HNO,
NO,
N,O
HO,
HZO‘
OH
Oi’W
NO
HO,
HO,
HOZNO,
HO,NOZ
CFCI:
CF,CI 1
Cl
Cl0
Cl0
CH,
HZ
HO,
OH
Cl0
CIONO,
HOI
OH
0
N
N
ccl,
CH ,CCI,
CH,CCl,
CH,Cl
CH,CI
CHF,CI
CHF,Cl
-t
+
+
+
+
+
+
+
+
+
02
03
N,
02
HI0
0
H
0
0.3
03
HO,
OH
0
03
0,
OH
OH
O(‘D)
HO,
OH
CH,
CH,
HO,
03
NO,
OH
O(‘D)
W’D)
03
0
NO
Cl
Cl
Cl
HCI
NO,
0
Cl0
HOCI
HOC1
NO
0,
O(‘D)
O(Q)
OH
O(‘D)
OH
O(‘Dt
OH
-4 0
- 262
- WP)
-+ o(.3P)
- 20H
-* H
-% HO
- OH’
- HO,
- OH
- H,O
--t H,O
-- NO
- NO,
- NO,
-* NO,
,t& HNO,
- 7NO
- H201
- H,O
--+ CH;
- CH.3
- NO2
- OH
,t&
4
HOZNO,
HO,
- HZ0
- 3Cl
- 2CI
- Cl0
- Cl
- Cl
- CH,
- H
-+ 0,
-* Hz0
& CIONO,
- products
- HOCI
- Hz0
- OH
- N
- Nil
- 4Cl
- 3CI
- 3Cl
- Cl
- Cl
- Cl
- Cl
CF,CICFCI? + O(‘D) -J. 3CI
NO, + NO, -f-k NO I 5
+ Nz
+ 02
+ 0,
+ 0:
+ 0,
+ 0,
+ 02
+ 0
+ 0,
+ 0;
+ 0,
+ H,O
+ 0,
+ HO2
+ H,O
+ OH
+ OH
+ 20?
+ NO,
f 0, +
+ 0,
+ 0:
+ NO2
+ HCI
+ HCI
+ HCI
+ Cl
+ 02
4 Cl0
+ Cl0
+ 0
+ 0
(1)
(2)
(3)
(4)
(5)
(6)
(7)
w
(9)
( I (V
(11)
(12)
(13)
(14)
(15)
(16)
07)
(18)
(19)
(20)
(21)
(22)
(23)
(24)
(25)
(35)
NOI (27)
(2x1
w
(30)
(31)
(32)
(33)
(341
(35)
(36)
(37)
(38)
(39)
(40)
(41)
(42)
(431
(44)
(45)
(46)
(47)
(4x1
(4%
(50)
(51)
(52)

378 D. J. LARY AND J. A. PYLE
Table I. (conrinu~d)
N+?s
Cl0 + Cl0
CI,O,
02 + hv
OS + hv
OS + hV
NO + hv
NO? + hv
NO, + hv
NO, + hv
HW t- hv
NP, + hv
HOzNOz + hv
N,O + hv
CIONO, + hv
ccl, + hv
CFCI, + hv
CF,CI 2 + hv
CHF,Cl + hv
CFzCICFClz + hv
HOC1 + hv
CIZO, + hv
CH,Cl + hv
CH,CCI, + hv
HCl + hv
H2O -I- hv
H,O, + hv
Y NO, +
-K Cl,Oz
A Cl0 +
- 0 +
- 0 2 +
- 0, +
- N +
- NO +
- NO +
- NO, +
- NO2 +
- NO, +
- NO2 f
- N
- CtZ+NOs
+
- 4Cl
- 3Cl
- 2CI
- Cl
- 3Cl
- Cl +
- cloz +
- CH, +
- 3CI
- H +
- H +
- 20H
NO2
Cl0
0
O(3P)
O(‘D)
0
O(lP)
02
0
OH
NO,
HO,
O(‘W
OH
Cl -
Cl
Cl
OH
(531
(54)
(55)
(56)
(57)
(58)
(59)
(60)
(61)
(62)
(63)
(64)
(65)
(66)
(67)
(653)
(69)
(70)
(71)
(72)
(731
2Cl + 0, (74)
(751
(76)
(77)
(78)
(79)
4.1. The Partitioning of Reactive Oxygen
The levels of stratospheric ozone depend on two photolytic processes. Firstly, there
is production of ozone due to the photolysis of molecular oxygen, jO,, which takes
place at 1 < 242 nm (and therefore is not affected by the ground albedo). Figure 2
shows the impact on j0, of including the diffuse radiation field. As would be
expected, the enhancement in j0, due to an inclusion of the diffuse radiation field
increases with the atmospheric pressure. However, the large increase in j0, which
occurs in the troposphere and lower stratosphere, has a relatively small impact
since the absolute magnitude of j0, is small due to the strong attenuation at higher
altitudes of solar radiation with A < 242 nm. On the other hand, the increase above
30 km can be very significant, as discussed later. Secondly, the ozone concentration
depends on the photolysis of ozone itself, also shown in Figure 2. Photolysis of
ozone at I < 310 nm (jog) produces 0( ID) and is enhanced by the diffuse radia-
tion field in a similar manner to jOZ. Photolysis of ozone at 1> 310 nm (j0,) pro-
duces O(“P). j0, is sensitive to the ground afbedo and a high ground reflectivity
can lead to a significant increase in the levels of O(3P).
To put the importance of these two processes in context, if ozone is assumed to

DIFFUSE RADIATION, TWILIGHT, AND PHOTOCHEMISTRY - I 379
1
‘LI
10 5
E
100
(With Scattering)/(Without Scattering)
lOc--i-1; i
1
a
10
(With Scattering)/~Without Scattering)
b) x c 310 nm
1 2 J 10
60
30”N. Equinox
50
-k
- A=O.O
--- *=a3
$0
x=30”
j%*
* 30
20 -.
-.
*-.
104
.
i
1
a 5
10
(With Scattering)/(Nithout Scattering)
d) For all X
1 p 3 10 e
60 ”
I 30”N. Equinox
50 P&/Uh+jO3*)
?:,o
53
/ A-O.0
A=03
; x=30”
N30 ‘,
1
-0
10 E
e
100
1
-0
10 F
z
100
(With Scattering)/(Without Scattering)
Fig. 2. The effect of diffuse radiation on the calculation of the phototysis of molecular oxygen and
ozone for a solar zenith angle of 30”. and ground albedos of 0.0 and 0.3.
be in photochemical equilibrium, and only the pure oxygen Chapman photo-
chemistry is considered, then the ozone ~quilib~um concentration is given by
[“.ilrquilibrium K
i--
jO2
jo, +io; ’ (4)
Two points can be made about the jO,/(jO, + j0:) ratio. Firstly, the zenith angle
dependencies of j0, and j0; are different from that of jO,, due to the different
spectral regions involved. Secondly, the ground albedo has no effect on jO,, little
influence over jog, but a major effect on j0, (Figure 2). Figure 2(d) shows the
large effect which scattering has on the jO,/(jO, + j0;) ratio, particularly in the
lower atmosphere; this is mainly due to the increase in j0,. For an increase in the

380 D. J. LARY AND J. A. PYLE
albedo from 0.0 to 0.3 (which is close to the global average), Figure 2(d) shows
that, for the Chapman scheme, the equilibrium concentration of ozone should
actually decrease at low altitudes, due to an enhancement of ozone photolys~s at
I > 310 nm (see Equation (3)).
Equation (3) is however an approximation, and the ozone concentration is also
controlled by several catalytic cycles. The ozone destruction caused by these cycles
depends on the levels of atomic oxygen, and a range of other, very reactive, short
lived constituents. The concentrations of these constituents are in turn controlled
by photolysis, and therefore depend on the diffuse radiation field as well. When
these catalytic cycles are incorporated, including the diffuse radiation field with a
ground albedo of 0.3 leads to a net increase in the stratospheric ozone concentra-
tion predicted by the model. Since reflection from the earths surface enhances
ozone photolysis the increase in the ozone equilibrium concentration is greatest
when little or no ground reflection can occur. Notice that over the ocean the atbedo
is typically CO.1 and therefore, all other things being equal, we would expect higher
ozone production than average in these regions. Likewise over continental regions
with higher albedos the ozone production would be somewhat lower than average.
Most of the reactions which constitute a net loss of odd-oxygen involve atomic
oxygen (Froidevaux et al., 1985; $8.2 WMO, 1986) it is therefore informative to
consider the effects of diffuse radiation on the [O(3P)]/[03] ratio, which is given by
the simple expression
io, + “KG 1wp)l = l-03 + jof
P31 k, (M] [02] = 0.21 k, [O,]” . (5)
As expected, the enhanced ozone photolysis due to an inclusion of the diffuse
radiation field leads to more odd-oxygen in the form of atomic oxygen, particularly
in the lower atmosphere (Figure 3). The enhancement of the levels of O(3P)
decreases with increasing solar zenith angles, and increases with the level of ground
reflection, which are both characteristics of the solar radiation field at 1> 310 nm.
On the other hand, the enhancement of O(‘D) concentrations is characteristic of
the solar radiation field at 1 < 310 nm, the enhancement is not dependent on the
ground albedo and increases rapidly with the solar zenith angle (Figure 4). The
reason for this behaviour can be seen by examining the expression for the [O(‘D)]/
[O,] ratio
(6)
The prime source of O( ‘D) is the photolysis of ozone by solar radiation with
1< 310 nm. The enhancement of the [O(‘D)]/~O(3P)] ratio and of the [O(3P)]/~O~]
ratio have totally different zenith angle dependencies, which characterise the differ-
ent wavelength regions responsible for producing O(lD) and O(3P). This again
highlights the importance of an accurate description of the diffuse ultraviolet radia-

DIFFUSE RADIATION, TWILIGHT. AND PHOTOCHEMISTRY - I 381
[~(3P)l/I~31 A=O.O
(With Scat.)/(Without Scat.)
[W3P)1/1031 A=0.3
(With Scat.)/<Without Scat.)
Zenith Angle Zenith Angle
Characteristic of X > 310 nm.
Fig. 3. The effect of diffuse radiation on the calculated [O(3P)]/[0,] ratio for a ground albedo of 0.0
and 0.3. for the spring equinox at 30” N.
A=O.O b) A=0.3
(With Scat.)/(Without Scat.) (With Scat.)/(Without Scat.)
‘40 40 50 60 70
Zenith Angle Zenith Angie
Characteristic of b c 310 nm.
Fig. 4. The effect of diffuse EidkitiOil on the calculated [O( ‘D)]/[O( jP)J ratio for a ground abedo of
0.0 and 0.3, for the spring equinox at 30” N.
tion field for 3, < 310 nm, particularly during twilight. If such a description is not
included, then the model calculation of 0( ‘D) may be in error. Notice that the most
important consequences will again be in the middle stratosphere where the
changes, while relatively modest, have the largest impact on subsequent chemical
processes.

382 D. J. LARY AND J. A. PYLE
4.2. The Partitioning of Reactive Nitrogen
Reactive nitrogen plays an important part in stratospheric photochemistry. The
primary source of stratospheric odd-nitrogen is the reaction of O(rD) with N,O.
The model predictions of reactive nitrogen depend on the overlap of the N,O and
O(‘D) distributions which reach a maximum in the tropical mid-stratosphere
(Crutzen and Schmailzl, 1983). O(‘D) undergoes a diurnal cycle, and is most
abundant for low solar zenith angles. An inclusion of multiple scattering generally
leads to an increase in jN,O and O(rD) of at least 5% at ail altitudes (N,O photo-
lysis and 0( “D) production both occur at ,I< 310 nm) (Figure 5).
Turning to the partitioning in the NO, family, the [NO]/[NO,] ratio can be
written
(7)
The fraction of NO, present as NO, (Figure 6) is decreased when an accurate
treatment of the diffuse radiation field is included for four main reasons, all of
which are dependent on the radiation field for A > 310 nm. They all depend on the
ground reflection of direct and diffuse radiation.
h < 240 nm
60
ooooo A~0.3 -
50 x=30” Yl.
-40
E
24
N 30
20
10
(With Scattering)/(Without Scattering}
Chamcteristic of X < 310 nm.
Fig. 5. The effect of diffuse radiation on the photolysis of N20 for a solar zenith angle of 30”.

DIFFUSE RADIATION, TWILIGHT, AND PHOTOCHEMISTRY - I 383
d [NOl/[NOzl A=O.O
(With Scet.)/(Without Scat.)
&3 40 50 60 70 80 3x0
‘40 40 50 60 70 80 9d0
Zenith Angle
b) b’Ol/‘[NOZl A=0.3
(With Scat.)/(Without Scat.)
‘40 I * 40 I 50 I 60 .--T- 70 d, 80 9d0 1
Zenith Angie
Characteristic of X 5 310 nm.
Fig. 6. The effect of diffuse radiation on the calculated [NO]/[NO,I ratio for a ground albedo of 0.0
and 0.3, for the spring equinox at 30” N.
(1) The levels of NO, are decreased by the photolysis of NO,. This mainly
occurs for n < 410 nm, and is therefore enhanced by the ground reflection
of the direct and diffuse solar flux.
(2) The levels of NO, are decreased by its reaction with atomic oxygen. The
levels of atomic oxygen are enhanced by the diffuse radiation field, and by
ground reflection, sinze ozone photolysis is the main source of atomic
oxygen and can occur for 2 > 310 nm.
(3) The levels of NO, are increased by the reaction of NO with ClO. However,
the fraction of CIO,T present as Cl0 is reduced by an inclusion of the diffuse
radiation field, and ground reflection (see Section 4.3).
(4) The levels of NO, are increased by the reaction of NO with HO,. However,
the fraction of HO, which is present as HO, is reduced by an inclusion of
the diffuse radiation field, and ground reflection (see Section 4.4).
4.3. The Partitioning of Reactive Chlorine
The ~Cl]/]ClO] ratio (Figure 7) is given by
[ela k,, PI + MN01
WI k&,1 (8)
Unlike the [O( “P>]/[O,], [O( ‘D)]/[O,], and [NO]/[NO,] ratios, the [Cl]/[ClO] ratio
does not contain any photolysis rates directly. The dependence of the [Cl]/]ClO]
ratio on the radiation field is indirect, and arises because the 1eveIs of both atomic
oxygen, and NO, are determined by photolysis. As seen in the preceding section,
both 0 and NO are particularly affected by the solar flux in the region 1 > 310 nm.
Hence, as expected, the enhancement of the calculated [Cl]/[ClO] ratio due to the

384 D. J. LARY AND J. A. PYLE
lcll/~clol A=O.O
(With Scat.)/(Withcut Scat.)
Zenith Angle Zenith Angle
(km)
Fig. 7. The effect of diffuse radiation on the calculated [Cl]/[ClO] ratio for a ground albedo of 0.0
and 0.3, for the spring equinox at 30” N.
inclusion of diffuse flux in the model calculations is characteristic of this spectral
region, i.e. it depends on the ground albedo and decreases with increasing solar
zenith angles.
4.4. The ~~~i~~~~i~g o~Re~c~ive ~yd~ogerl
The (OH]/[H02] ratia is given by
Like the ~Cl]/[ClO] ratio, the expression for the [OH]/[HO~] ratio does not contain
any photolysis rate terms, and the effect of diffuse radiation is indirect. The amount
of HO, which is present as OH is favoured by relatively high levels of atomic
oxygen which is enhanced mainly by the photolysis of ozone at A > 310 nm. Conse-
quently, the enhancement of the [OH]/[HO,] ratio is characteristic of A > 310 nm,
i.e. it is sensitive to the ground albedo and is greatest for small zenith angles (Figure
8).
The total mount of HO, present depends on the photolysis of I-I,0 (at ,I < 200
nm), H70Z (at A < 3.50 nm), and the reaction of O(‘D) with H,, CH, and HzO.
These are all processes which are particularly sensitive to the ultraviolet radiation
field, where the multiple scattering of solar radiation by air molecules is of great
importance, and consequently, there is an increase in the levels of HO,, predicted
by the mode1 in the lower atmosphere when the effects of multiple scattering are
included. It is interesting to note that the partitioning of HO,(=OH + HO,)
between OH and HO, depends on I > 310 nm, whereas the production of HO,
depends mainly on A < 310 nm.

DIFFUSE RAL>IATION. TWILIGHT, AND PHOTOCHEMISTRY - I 385
Zenith Angle Zenith Angle
Character&tie of 1 > 310 nm.
Fig. 8. The effect of diffuse radiation on the calculated [OH]/[H02j ratio for a ground al&do of 0.0
and 0.3. for the spring equinox at 30” N.
5. Model Predictions of Stratospheric Ozone
The previous sections considered the effect of diffuse radiation on the partitioning
between radicals involved in ozone destruction. This section examines the subse-
quent effect on the calculated concentration of stratospheric ozone.
A matter of concern over the past few years has been the 40 km ozone problem.
Models have tended to systematically underestimate ozone levels there (e.g. WMO,
1986), despite the fact that the chemistry has been thought to be both simple and
understood in that region. The magnitude of the discrepancy appears to be very
model dependent, because it depends on the feedback between radiation and
chemistry which may or may not be included in the various models, the photo-
chemical reactions considered, and the kinetic data used. For example, Natarajan
and Callis (3 989) showed that the use of the new kinetic data from DeMore et d.
(1987) for the reaction of OH + HO,, led to a significant reduction in the discre-
pancy between model ozone calculations and observations.
The conclusion of the model intercomparison presented in WMO (1986) was
that models underestimate upper stratospheric ozone by 30 to 50%. A similar
intercomparison was carried out for WMO (1990) where the models were found to
systematically underestimate the amount of ozone by 10 to 50%. Therefore, even
with the use of the most recent kinetic data, there is still a discrepancy, of at least
lo%, between many model predictions and observations of ozone.
A number of su~estions other than an inadequate kinetic database for the cause
of this discrepancy have been advanced. For example, Pyle and Zavody (1990)
considered the problem in terms of systematic errors which arise when averages, be
they global, zonal or even regional, are taken in numerical models. They concluded
that this source of error is in general insufficient to explain the problem. On the

386 D. J. LARY AND J. A. PYLE
other hand, Slanger et al. (1988) have suggested that photolysis of vibrationally
excited 0, could provide the missing source of ozone and Toumi et al. (1991) have
found excellent agreement in a model calculation between observed and calculated
ozone. However, they point out that the calculation is sensitive to a number of
important assumptions for which corroborative laboratory data is not available.
The Slanger mechanism appears to be an important breakthrough in under-
standing upper stratospheric ozone. Nevertheless, there are still major differences
between modelled photolysis rates (see for example the two-dimensional model
intercomparison of Jackman et al. (1988)) an d we turn to the impact of these on the
calculated ozone.
Much of the attention aimed at resolving the 40 km ozone problem has been
focused on the photolysis of ozone since the major loss processes of odd-oxygen
involve atomic oxygen (Froidevaux et al., 1985; $8.2 WMO, 1986). However, as
seen earlier, the ozone equilibrium concentration is also to a first approximation
proportional to ji0, (Equation (3)). Therefore, particular attention needs to be
paid to the calculation of molecular oxygen photolysis as well. The photolysis of
molecular oxygen in its ground state occurs exclusively for A < 242 nm. This is a
region of the spectrum which needs to be treated with particular care, and which
some radiative transfer models treat incorrectly. For example, the diffuse radiation
field at 40 km and k < 242 nm measured by Herman and Mental1 (1982) was not
reproduced by the model of Luther and Gelinas (1976) but was reproduced by the
radiative transfer model used in this study (Lary, 1991; Lary and Pyle, 1991).
The ozone concentration is also sensitive to the photolysis of NO,. The reason
for this is twofold. On the one hand the NO-NO, catalytic cycle destroys ozone,
and on the other, the photolysis of NO, produces odd-oxygen.
Figure 9 shows that inclusion of multiple scattering increases the NO, photolysis
rate by at least 50% throughout the stratosphere. As a result, the rate of odd-
oxygen production, and the ozone concentration, is also enhanced.
This section presents the result of a model/data intercompa~son of ozone for
the spring equinox at 30” N. Figure 1Oa) shows a comparison of the model ozone
profile and the measured ozone climatology, while Figure lob) shows the per-
centage deviation of the model ozone concentration from the climatology. The
appropriate temperature and density data from the climatology of Barnett and
Corney (1985) (Map Handbook 16) were used, and the kinetic data were taken
from DeMore et al. (1990).
An inclusion of diffuse radiation in the photochemical radiative transfer model
increases the calculated amount of solar flux available for photolysis. The amount
of scattering which occurs is proportional to the total number density, and so
increases with pressure. Therefore, the underestimate of photolysis is most severe
in the lower stratosphere and troposphere. This is consistent with Figure 10 where
the solid line in each plot is for a model calculation which ignores the effects of
diffuse radiation and ground reflection, and the dashed lines are for model calcula-
tions which includes the effects of diffuse radiation for three different values of the

DIFFUSE RADIATION, TWILIGHT, AND PHOTOCHEMISTRY - I 387
60
50
- E 40
s V
N 30
20
10
1
I
h < 410 nm
2 3 4 5 6 7??10
I
I ~ A=0
I _ ~ A=0.3
I
I
1
x=30” 1
‘d
10 F
4
100 \
1
\
” - - -d
30”N, Equinox
\
2 3 4 5 rn
’ (With S ca tt ering)/(Without Scattering) ’ ”
Fig. 9. The effect of diffuse radiation on the calculated NO, photolysis rate for ground albedos of
0.0 and 0.3.
ground albedo (0.0,0.2, and 0.4). Note that the difference between the model with
and without a treatment of the diffuse flux is on the order of 10%. Inclusion of
diffuse radiation seems to bring models and observations into better agreement.
A number of processes are involved in determining the ozone distribution.
Figures 2 and 9 show that the photolysis of 0, and NO,, both of which lead to
ozone production, increase when scattering is included and we believe both of
these processes are playing important roles. The effect of scattering on oxygen
photolysis decreases with increasing altitude while the importance of the nitrogen
oxides in controlling the ozone concentration also decreases above the mid-strato-
sphere. Both of these factors explain why inclusion of scattering makes the most
impact on the ozone concentration below 40 km. It should also be noted that the
O(3P)/0, ratio is increased when scattering is included. Since many of the impor-
tant ozone destruction cycles are rate limited by reactions involving Ot3P) this
should decrease the calculated 0, concentration. It is clear from Figure 10 that this
process is not as important as the direct impact on the photolysis of O2 and NO,.
To summarise, if a detailed treatment of diffuse radiation is included in the
model, then in the region where ozone is under photochemical control at close to
40 km, the discrepancy between the model calculations and observations is
reduced (in this case to approximately zero at 40 km); the inclusion of diffuse
radiation always increases the 0, concentrations calculated by a numerical model
with a ground albedo of less than 0.4. Note that this is a general result. Further
important changes in the calculated ozone distribution will, of course, result from
the inclusion of new mechanisms. For example, the Slanger mechanism modelled

D. J. LARY AND J. A. PYLE
No Scattering
_____ A=0.4
+++++Climatology
ffeating % Pitt3 [lB88]
b)
-40 -30 -20 -10 0 10 2
50 '
30”N, Equino
45-
3%
No Scattering
-- A=O.O
_ _ A=0.2
.____ A=0.4
30
-40 -30
5% Difference from Climatology
Fig. 10. The effect of diffuse radiation on model ozone calculations.
by Toumi et al. (1991) appears to play a very important role in determining the
ozone distribution, not just in the stratosphere, but also in the mesosphere, where
multiple scattering is less important.

DIFFUSE RADIATION, TWILIGHT. AND PHOTOCI-IEMISTRY - 1 389
6. Diffuse Radiation and Polar Photochemistry
At high latitudes during winter most of the photolysis which takes place is due to
sunlight incident on the atmosphere at very high zenith angles. This has particular
relevance to the polar ozone issue, since for ozone destruction to take place atmos-
pheric halogen constituents must be in their reactive forms. These short lived radi-
cals are only present when photolysis takes place, and so if an accurate description
of ozone depletion is to be made by a numerical model it is vital to have an accurate
description of the twigliht radiation field. For example, it is now accepted that the
Cl0 dimer reactions proposed by Molina and Molina (1987) play a dominant role
in polar ozone loss (WMO (1990) and references therein). The rate limiting step in
the catalytic cycle is the photolysis of the Cl0 dimer, C1,02.
Cl202 + hv - Cl00 + Cl
Figure 11 shows the diurnal average of jCl,O, at the winter solstice, and how much
of the total photolysis is occurring at solar zenith angles greater than 75” and 90”.
Note that up to 45% of Cl,Oz photolysis which takes place in the lower strato-
sphere at this time of year occurs for solar zenith angles greater than 90”. As a
result, models which do not include the effects of multiple scattering during twilight
will underestimate the ozone destruction at high latitudes. As the model used in
this study underestimates the radiation field for zenith angles greater than 93”, the
amount of photolysis which occurs at zenith angles greater than 90” is even more
than that shown in Figure 11.
7. ConcIusion
This paper has described photochemical calculations carried out with a detailed
photolysis scheme including a detailed treatment of multiple scattering and the
earth’s curvature, following Meier et al. (1982) and Anderson (1983). Some
general examples have been studied in detail. These have included the impact on
partitioning between various radicals after the inclusion of an accurate treatment of
diffuse flux in the model. The study has shown that diffuse radiation is particularly
important when calculating the photolysis which takes place at il < 310 nm. Atten-
tion was drawn to the different zenith angle dependence of diffuse radiation for the
two spectral regions 1< 310 nm and 1> 310 nm, and the effect that this has on
stratospheric chemistry. In general, when radiation at wavelengths less than 310 nm
dominates the photochemistry, the impact is greatest at high zenith angles and the
albedo has little effect. The opposite is true if radiation longwards of 310 nm is con-
sidered, where the impact of the diffuse field is greatest at low zenith angles and for
high albedos.
The effect on the model ozone profile was considered. It was shown that when
the latest kinetic data is used together with a detailed treatment of multiple scatter-
ing, then the discrepancy between the observed and calculated ozone profile
between 30 and 50 km is less than 10%. Of more general significance, given the

390 D. J. LARY AND J. A. PYLE
a) Diurnally averaged jCl202 at the winter solstices’)
.’
3 -30 0.
a -20
- 10
Latitude
b) Percentage of Cl202 photolysie occuring for solar zeuitb angles > 75
Latitude
c) Percentage of Cl202 photolysis occuring for solar zenith angles > 90
c \ /
60 c \ .l
s 50-
al 40-
3 : z 30
Q -
20 +
V
- 80
E -50
=40 c
13 -39
la0 -20
Note that in this region of particular importance for the polar ozone Issue
upto 45% of Cl202 photolysis is occurlng for solar zenith angles > 98 degrees.
The Solstice
Fig. 11. A latitude-height cross section of Cl,O, photolysis at the winter solstice.

DIFFUSE RADIATION, TWILIGHT, AND PHOTOCHEMISTRY - I 391
present differences between models, is the fact that inclusion of a detailed radiation
scheme always increases the calculated ozone for an albedo of less than 0.4. Some
of the discrepancy reported between models and observed ozone around 40 km
seems likely to be due to an incorrect treatment of radiation.
The importance of correctly including multiple scattering for solar zenith angles
greater than 90” when modelling polar ozone was also demonstrated. For example,
it was shown that in polar regions up to 45% of jCl,O, photolysis (the rate limiting
step for polar lower stratosphere ozone depletion) is occurring for solar zenith
angles greater than 90”. A detailed treatment of multiple scattering at these solar
zenith angles is particularly important.
Acknowledgements
David Lary thanks SERC for a studentship. This work was partly supported by the
CEC under grant STEP0016 from DGXII. This work forms part of the NERC
U.K. Universities Global Atmospheric Modelling Project.
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