Journal of Atmospheric Chemistry 13: 393-406, 1991.
0 1991 Kluwer Academic Publishers. Printed in the Netherlunds.
393
Diffuse Radiation, Twilight, and
Photochemistry - II
D. J. LARY and J. A. PYLE
Department of Chemistry, University of Cambridge, Cambridge CB2 IEW, U.K.
(Received: 9 July 1991)
Abstract. A photochemical scheme including a detailed description of multiple scattering up to solar
zenith angles of 96’ has been used to’ study a number of different datasets. The good agreement of the
model with these datasets and the improvement over previous intercomparisons emphasise the impor-
tance of both the diffuse radiation field at wavelengths below 310 nm and multiple scattering at solar
zenith angles greater than 90’. These features are ignored in some photochemical models but prove to
be very important in modelling photochemistry at dawn and dusk.
Key words: Multiple scattering.
1. Introduction
In a companion paper, Lary and Pyle (1991) have described a radiation scheme
which has been developed for use in atmospheric photochemical models. The
scheme is based on Meier et al. (1982) and Anderson (198 3). It includes the effects
of ground reflection and a detailed treatment of multiple scattering up to a solar
zenith angle of 96”. As such, it is particularly appropriate for the study of photo-
chemical phenomena at dawn and dusk, as well as in polar latitudes. In the earlier
paper a number of general features were discussed, in particular, the contrasting
behaviour of diffuse radiation at wavelengths above and below 310 nm. Multiple
scattering in the latter region is often not considered when calculating photolysis
rates. The effect on the partitioning between the radical families was described in
detail, as well as the impact on the calculated ozone in the model. Throughout, the
role of diffuse radiation was emphasised and the importance of an accurate treat-
ment of multiple scattering at wavelengths less than 310 nm was stressed.
In this paper we consider the scheme in detail, examining a number of cases
where either the radiative transfer model can be validated or where the use of the
model allows data to be interpreted in greater detail. We consider a number of
specific cases. These include the radiative flux measurements of Herman and
Mental1 (1982) which allows the model to be validated; balloon and satellite mea-
surements of the diurnal variation of nitrogen oxides, which provide a good test of
the model treatment of the dawn and dusk transitions; and the ground based ultra-
violet measurements of Lubin et al. (1989). These are now described in turn.

394 D. J. LARY AND J. A. PYLE
2. Comparison with Stratospheric Ultraviolet Measurments
A good test of any radiation model is, of course, the measured radiation field as a
function of wavelength. Herman and Mental1 (1982) made such measurements
from a balloon at a float altitude of 40 km and a solar zenith angle of 41.2”. Two
separate systems were used, one pointed directly at the sun, and the other oriented
in six different directions away from the sun to determine the amount of scattered
solar flux (Figure 1).
The scattered flux within the atmosphere can be estimated by integrating the
measured specific fluxes over 4n steradians. Herman and Mental1 measured
specific fluxes in one plane in six specific directions (Figure 1). To do the integra-
tion they performed logarithmic interpolation between adjacent pairs of measure-
ments. In addition they assumed that the specific flux in the direction of the sun is
at least as large as F6 {the flux from direction 6 measured by Herman and Mentall)
in Figure 1. As pointed out by Herman and Mentall, since the maximum scattered
flux is assumed to be F,, the resulting integration is an underestimate of the total
scattered flux. This is found to be the case (compare the Herman and Mental1 data
in Figure 2 with the model results). In an attempt to quantify the underestimate
resulting from the assumption that F6 was the maximum flux, the scattered flux in
the numerical model was reduced by 80% (dashed curve in Figure 2). It can be seen
that this produces much better agreement with the data between 210 and 300 nm.
The earlier theoretical work of Luther and Gelinas (1976) considered the flux
ratio at 40 km for a solar zenith angle of 60”, and a range of ground albedos. Their
study reproduces the contribution from diffuse flux for 2 > 300 nm, but shows no
contribution from diffuse flux for Iz < 210 nm, contrary to the measurements of
Herman and Mental1 (1982). R. J. Gelinas pointed out that this is probably due to
the bin-averaged cross sections used in the Schumann-Runge bands of oxygen
Fig. 1. The measurement geometry used by Herman and Mentall (I 982).

DIFFUSE RADIATION.TWILIGHT,ANDPHOTOCHEMISTRY-II 395
x 190 200 210 220 230 240 250 260 270 280 290 300 310 320
,’
:’
i
J \
\
\
Yil
\ i
x=41.2”, P=1.5 mb.
I / I/, 3 / 11 1 / 8 I 11 I
t
I
IO -I
IO -2
IO -3
190 200 210 220 230 240 250 260 270 280 290 300 310 320
Wavelength (nm)
Fig. 2. The diffuse to direct solar flux ratio at 40 km for a solar zenith angle of 4 I .2”, estimate from
measurements (squares) and calculated (lines)
(private communication to Herman and Mental1 (1982). This study uses the para-
meterisation of Frederick (1985) to calculate the absorption cross section for the
Schumann-Runge bands of molecular oxygen.
Notice that the ratio is very wavelength dependent, becoming larger at wave-
lengths greater than 300 nm and in the ultraviolet window at around 200 nm. The
models has been run using a standard atmosphere ozone profile to calculate the
ratio of scattered to direct flux at 40 km and a zenith angle of 41.2”, the conditions
of the Hermann and Mental1 (1982) measurements. Figure 2 shows that the wave-
length dependence of the ratio is well reproduced by the model.
Two conclusions can be drawn from the example. Firstly the model appears to
be validated by the measurements. Secondly, there is clearly an important role
played by the scattered radiation at wavelengths below 300 nm. In particular, the
contribution to photolysis by diffuse radiation in the important window region
around 200 nm is certainly not negligible and should be included in photolysis rate
calculations.
Notice that the increase in the photolysis rate of 0, due to diffuse radiation
at these wavelengths is an important source of 0, (see Lary and Pyle (1991),
Figure 2).

396 D. J. LARY AND J. A. PYLE
3. The Diurnal Variation of NO and NO,
Nitric oxide is one of the few photochemically active gases for which there are mea-
surements with a high time resolution. In the sunlit stratosphere, NO is in immedi-
ate photochemical equilibrium with NO,. The reactions which give rise to the rapid
NO, = (NO + NO,) interchange are listed in Table I. If NO2 is in photochemical
equilib~um then d(NO,j/dt = 0, and the [NO1 to [NO,] ratio can be written as
WI WI + W2 -=
[NO,] k, [0,] + k,[ClO] + kJHOz1 . (1)
jN0, is a major term in this expression, and high time resolution measurements of
NO are an ideal test for appraising the accuracy of a photoche~cal radiative trans-
fer model.
Measurements of NO at sunset were made by Kondo et al. (1985, 1988) using a
balloon borne chemiluminescent instrument flown from Aire sur 1’Adour. The data
were considered by Roscoe and Pyle (1987) who were unable to match precisely
the zenith angle variation with their numerical model. Figure 3 shows results from
their paper. A photolysis scheme including no treatment of Rayleigb scattering
failed badly to reproduce the data. When the effect of Rayleight attenuation of the
direct beam was considered the agreement between model and data was improved,
but the model still calculates too large an NO concentration at high solar zenith
angles.
Figure 4 shows a comparison between measured NO and model calc~ations
using the present radiation scheme. Agreement between model and data is excel-
lent. It is clear that an accurate description of multiple scattering during twilight is
necessary to reproduce the details of the diurnal variation of short lived species
such as NO at dawn and dusk.
3.2. Satellite Measurements
Polar orbiting satellites on a sun-synchronous orbit always cross the equator at the
same local time. However, the measurements made in high latitudes cover a wide
Table I.
NO+O,
NO + Cl0
NO,+0
NO + HO2
1>410nm NO, + hv
NO, * 0,
NO, + NO,
NPs
- NO,+O,
- NO,+Cl
- NO+O1
- NO,+OH
- NO+0
- NO,+O,
JL N,OS
-Me NO, +NO,
(1)
(2)
(3)
it; jNOz
(6)
(7)
(8)

DIFFUSE RADIATION, TWILIGHT, AND PHOTOCHEMISTRY - 11
31St0.7km
397
I 1 I I , I I I L L I
80.7 02.5 84 4 86.3 88.1 89 9 91.8 93.7 95.5 97.3
SoiarangleIdegreesI
Fig. 3. Comparison of NO measurements made by Kondo et al. (1985) (points) with the model of
Roscoe and Pyle (1987) (solid line) and the same model with improved Rayleigh scattering (dashed
line).
82 84 86 88 90 92 94 96 98
1.0 I I I I 1 I I I I ! I I I 1.0
0 44”N, 19 September -_ q -_ 0 -_ -_-0 _. -0
0.8 - -‘,o - -. 0.8 ‘0 .a.
t!
0.6 - Y -
$ 0, 4
0.6
-A \ 4
cd b
7lo.4
\
- - LJ 0.4
iz \ \
'P \
0.2 - \ -
'\O
0.2
- Kondo et al. 1988. ‘\ • 0~~~
----- Model. ‘p
0.0 ---- ----- ____ 2*-o ______
(-----; ;-----,-----;---- 1 1 / I I I
0.0
82 84 86 88 90 Angz (D”,“,re,““,) 98
Solar Zenith
Fig. 4. Comparison of NO measurements made by Kondo et al. (1988) and model calculations in-
cluding a detailed treatment of multiple scattering.
range of zenith angles, and therefore, local times from which diurnal variations can
be constructed. Solomon et al. (1986) presented a similar reconstruction of the

398 D. J. LARY AND J. A. PYLE
NO, diurnal cycle (Figure 5) from LIMS. This was done by using the observations
of NO, made between 56” N and 84” N, over the period 1 May to 28 May 1979.
As a consequence of the dynamical stability over this period, the local variability in
NO, caused by atmospheric motions was very small, and did not overwhelm the
diurnal variation of NOz.
The model calculations presented by Solomon et al. (1986) in Figure 5 are as
follows: The dashed line is for a model assuming pure absorption and single scat-
tering, while the solid line is for a model obtaining columnar multiple scattering
with an albedo of 0.3.
The diurnal cycle reconstructed in this way is best termed a quasi-diurnal cycle,
since, for at least four reasons, no ‘real’ diurnal cycle of NO, which occurred during
May 1979 can simultaneously go through all the LIMS measurements. Firstly, no
single May diurnal cycle spans the solar zenith angle range 34” to 109”. Secondly,
the levels of NO, are sensitive to ozone, and there was a significant latitudinal gra-
dient, and temporal change, of ozone during May. Thirdly, the levels of NO, are
sensitive to temperature, and there was a temporal change in temperature during
the month (albeit small). Fourthly, since the sun never sets poleward of approxi-
mately 70” N during May, whereas there is still a diurnal cycle equatorward of
approximately 70” N, the partitioning of reactive nitrogen species will change with
latitude (for example, in the region of constant illumination, photolysis will lead to
much lower levels of N,O,).
This section compares the LIMS data with our photochemical model. Our
analysis differs somewhat from that presented by Solomon et al. (1986). In particu-
lar, we consider each latitude band separately and consider variations which may
have occurred during May. We will examine in detail the data at 68” N, where the
diurnal variation was most pronounced.
30 40 50 60 70 80 90 100 110
ZENtTH ANGLE (OEG)
Fig. 5. Observed variation in NO1 at 10 mb from 56” N to 84” N during May as a function of zenith
angle, zonally and 4-day averaged (Solomon et al. (1986) fig. 2~).

DIFFUSE RADIATION, TWILIGHT, AND PHOTOCHEMISTRY - II 399
A latitudinal gradient of ozone existed during May, with a monthly zonal mean
of approximately 6.9 ppmv at 56” N decreasing to less than 5 ppmv at 84” N. For
all latitudes there was also a temporal trend, with values at the end of May being
approximately 10% less than at the beginning of the month (Solomon et al., 1986).
In this study, the zonal monthly mean ozone at 10 mb was found by applying a least
squares fit to the LIMS and SBW ozone data for May, given by Russell et al.
(1986). If # is the latitude in degrees between 56” N and 84” N, then the zonal
monthly mean ozone concentration in ppmv is approximated by
(wilean = 11.08 - 0.0754. (2)
The latitudinal temperature gradient was very small compared to that of ozone, and
for any given day it did not exceed 4 K for the latitude band 56” N to 84” N, with
the mean for this latitude band of approximately 234 K. There was a temporal
temperature increase during the month of as much as lo-15 K (Solomon et al.,
1986).
This study assumed that, in accordance with the observations, there is a latitu-
dinal gradient in the zonal mean ozone concentration given by Equation (2) and
that there is a temporal change in ozone of 10% at all latitudes, i.e. ozone values on
1 May are 5% higher than given by Equation (2) and on 28 May are 5% lower than
given by Equation (2). The reactive nitrogen content of the model was then
adjusted for each latitude band in order to obtain a good agreement with the LIMS
NO, data. The model was able to reproduce well the NO1 measurements, as can be
seen in Figures 6 and 7.
The agreement of the model with the LIMS measurements was improved when
the rate constants for the OH reactions with HOz and H,O, were taken from
DeMore et al. (1990) instead of DeMore et al. (1987). This reflects the effect of
OH concentrations on the levels of HO, and HNO,, and hence the partitioning of
reactive nitrogen.
The effect of the planet’s changing solar illumination, and the temporal decrease
in ozone levels during May, can be seen in Figure 6. Each plot contains two curves,
one corresponding to a solar illumination at the start of May, with an ozone con-
centration 5% higher than is given by Equation (2) and the other corresponding to
a solar illumination at the end of May, with an ozone concentration 5% lower than
given by Equation (2). In each case, a model temperature of 234 K was used (i.e.
close to the monthly mean for May 1979.
3.2.1, 56’ N to 64 ’ N. Due to the seasonal evolution of the solar declination angle,
the terminator retreats southward during May as the height of summer is ap-
proached. This is reflected in the LIMS measurements of NO,. For example, in
Figure 6 (a) and (b), if the nighttime decay of NO, is examined it is clear which
measurements were taken at the beginning of May, and which ones were taken at
the end of May. Those made at the start of the month can extend up to solar zenith
angles of 109”, whereas at the end of May the maximum zenith angle had decreased

400 D. J. LARY AND J. A. PYLE
30 40 50 60 70 80 SO 100 110
. . . . . LIMS.
b) 60"N.
30 40 50 60 70 80 90 lQ0 '10
. ..=. LIMS.
12.
4
4,....,....~..,.,.,..,....,...,,....,....r
30 40 50 100 110"
40 50 60 70 80 QCI IQ0 110
. . . ..LIMS.
Q-~,..,...,,....,....,....,....,.,.,~
40 50
Z&ith yngle ‘~Degr~~s)
100 1104
Fig. 6. A comparison of the diurnal variation of NO2 at 10 mb observed by LIMS (squares) and
simulated (line) for 56’ N to 64” N during May 1979.

DIFFUSE RADIATION, TWILIGHT, AND PHOTOCHEMISTRY - II 401
-10
-0
Fig. 7. A comparison of the diurnal variation of NO2 at 10 mb observed by LIMS (squares) and
simulated (line) for 68” N during May 1979.
to approximately 104”. In like manner, the measurements made at solar zenith
angles close to 40” could only have been made at the end of May.
3.2.2. 68” N. The two model calculations shown in Figure 7 are for a solar illumi-
nation corresponding to 1 May. The lower dotted curve is for an ozone concentra-
tion typical of early May and a temperature of 234 K, while the upper solid curve is
for an ozone concentration typical of mid-May, and a tempera~re of 238 K. This
latitude band is interesting since the LIMS observations captured the swift sunset
increase in NO,.
Examination of Figure 5 shows that there was a slight offset between the in-
crease in the NO, measured by LIMS at solar zenith angles greater than 90” and
those modelled by Solomon et al. (1986). While there are still discrepancies, the
timing of the increase seems somewhat better in our calculations (Figure 7). The
details of our respective treatments of scattering may be playing some role here.
Figure 8 shows the effect of neglecting multiple scattering when calculatng the
diurnal cycle of NO,. It is interesting to note that the amplitude and shape of the
NO, diurnal cycle are both affected by this approximation.
The comparison of calculated NO, with observations of its diurnal variation
provide a good test of the treatment of radiation in the model. In the cases con-
sidered, generally very good agreement has been found for both the case of in situ
balloon observations and diurnal variations derived from satellite data.

402 D. J. LARY AND J. A. PYLE
May 1, 68”N, (0,)=6.29 ppmv.
Zenith Angle (Degrees)
Fig. 8. The effect of ignoring multiple scattering on the calculated diurnal variation of NO1 with
[O,] = 6.29 pp ppmv (see text for explanation).
4. Groundbased UV Measurements and Total Ozone
In the preceding two sections we have used observations of the ultraviolet radiation
field to validate our treatment of diffuse radiation, and observations of NO and
NO? to validate the performance of the radiation model at high solar zenith angles.
In this final section we turn to ground based observations of ultraviolet radiation
and use our model to interpret the data in terms of the total atmospheric ozone
abundance.
The ozone absorption cross section decreases by two orders of magnitude from
295 nm to 330 nm. As a result, UV-B radiation (280 nm to 320 nm) is very sensi-
tive to the total ozone column, whereas UV-A radiation (320 nm to 400 nm) is
relatively insensitive to the total ozone column. Therefore, a good index of ozone
depletion is the ratio of UV-B to UV-A irradiance at the earths surface. Measure-
ments of this ratio were made by Lubin et al. (1989) during the Austral spring of
1988. This study compares these measurements with model calculations.
During the Austral spring of 1988 two main factors gave rise to a change in the
noontime irradiance ratio, a change in the noontime solar zenith angle resulting
from the seasonal evolution of the solar declination, and a variation in the total
ozone column. For a given wavelength;much of the measured UV va~ability was
due to changing cloud cover. However, to a first approximation, the attenuation by
clouds of both 300 nm and 340 nm is the same, and so the variability in the irra-
dance ratio (h,, .mYLtl nm ) due to changing cloud cover cancels out (Lubin et al.,
1989). Consequently the structure of the irradiance ratio is a reflection of the varia-
tion in total ozone. The vortex, which contains the region of maximum ozone
depletion, is a dynamic entity and much of the observed variability in the irradiance
ratio was caused by the vortex edge moving over Palmer Station.
Figure 9(a) shows irradiance ratios calculated using two models. One is the
detailed radiative transfer model, while the other, Figure 9(b), contains no treat-

DIFFUSE RADIATION. TWILIGHT, AND PHOTOCHEMISTRY - II 403
270 290
Without
Scattering
No COSlne
correction
70
16
al. [1989]
14
.: 12 .- -d .:. . ..- z f , ‘. .-I
21 :
. :. ,. c--- . . . . .:. .:+ z-: :. . ‘. . Y” i 1 21
‘.. . . ,.-
C,’ .,.. . .: . . . . . . I
b
. . : _/ h IL . . . : . . 5 .<’ .,- . . :.. -: ... : . ..’ -2 ,.... ., o-t--w----, 0
250 270 290 310 330 35or-i700 850 270 290 310 ---- 330 350 37cP
Day of the year Day of the year
Fig. 9. Measurements of the UV-B/UV-A (X 100) irradiance ratio at the earth’s surface compared to
model calculations made with; (a) the detailed radiative transfer model, and (b) no description of
multiple scattering.
ment of scattering. In each case three different ozone profiles are used in the calcu-
lations. The first profile was the US Standard Atmosphere, with a total ozone con-
tent of 348 Dobson Units. This corresponds to a ‘normal’ atmosphere with no
ozone depletion. The second profile was taken from the balloon sonde measure-
ments made at Halley Bay (76” S, 27” W), on 26 September 1987 (Gardiner and
Farman, 1988), with a total ozone content of 218 Dobson Units. The third profile
was taken from the balloon sonde measurement made at Halley Bay on 13
October, 1987, and corresponds to one of the most severe ozone depletions on
record, with a total ozone content of only 157 Dobson Units. To put these profiles
into context, we note that the Antarctic ozone depletion was much less severe in
1988 than 1987. For example, the minimum values of the total ozone column
recorded at Halley Bay during 1988 were only a little below 200 Dobson Units,
with a mid-September to mid-October average of around 200 Dobson Units.
There are very large differences between the model calculations made with and
without a treatment of multiple scattering. The calculations made without including
the effects of scattering can only be reconciled with the observations taken before
mid-November if the ozone column was very low, significantly less than 200
Dobson Units. Indeed, an ozone hole deeper than that observed during 1987
would be required to explain the calculations which do not include multiple scatter-
ing. However, the ozone observations made during 1988 do not support this. On
the other hand, the calculations including scattering do agree with the observations.
When multiple scattering is considered it can be inferred from the measured irra-
diance ratio that the total ozone content did not go below approximately 200
Dobson Units and that the maximum irradiance ratio was seen just after the middle
of October when the levels of total ozone were at their lowest. By the middle of
November the irradiance ratio dropped close to the value calculated for a total
ozone content of 350 Dobson Units, i.e. there was a relatively early recovery from
the shallow 1988 ‘Ozone hole’.

404 D. J. LARY AND J. A. PYLE
Figure 10 shows the total ozone column above Palmer station which can be
inferred from the measured irradiance ratio. A correction was made for the cosine
response of the instrument so that a direct comparison could be made between the
model and the measured irradiance ratio. Figure 10 also compares the inferred
total ozone with the TOMS measurements for 1988 (These are the TOMS version
5 data, courtesy of the Geophysical Data Facility, Rutherfored Appleton Laborato-
ry). Since the irradiance ratio measured by Lubin et al. (1989) was an inst~taneo~s
value (noon), Figure 10 also includes the minimum and maximum total ozone
values observed by TOMS for 64” S.
The radiative transfer model which includes a description of multiple scattering
(Figure 10(a)) is in good agreement with the TOMS measurements. However, it is
interesting to note that the largest discrepancy is during October and early Novem-
ber (i.e. before day 300 when the noon time zenith angles are still rather large). This
is in line with the concern that the TOMS version 5 dataset underestimates the total
ozone column at large zenith angles (Lefevre and Cariolle, 1991).
5. Conclusions
A photoche~cal scheme including a detailed description of multiple scattering up
to solar zenith angles of 96” has been used to study a number of different datasets.
Measurements of the ultraviolet radiation field made by Hermann and Mental1
(1982) agree well with the model. They emphasise the importance of the diffuse
radiation field at wavelengths below 310 nm, ignored in some models.
Diurnal variation measurements provide a very good test of a radiative transfer
model at high solar zenith angles. Comparison between two datasets have been
described. The model agrees very well with the diurnal variation of NO as observed
7
9400 400
e
iI
&lo 9 $09
2
w
QZOO 200
100 1QQ
230 280 300 320 340
Day of the year
Fig. 10. TOMS Measurements of total ozone compared to the values of total ozone inferred from
two sets of model calculations; (a) with multiple scattering, and (b) without multiple scattering. -
inferred ozone column, + * * 7 TOMS (64” S, 65” W), ------- TOMS min./max. for 64” S.

DIFFUSE RADIATION, TWILIGHT, AND PHOTOCHEMISTRY - II 405
from a balloon borne instrument (Kondo et al., 1985/1988). This is a marked
improvement on earlier calculations (e.g. Roscoe and Pyle, 1987). Secondly, com-
parison with satellite measurements of NO2 is also very good. Once again the high
zenith angle transition is captured well, and appears to be better than that obtained
in previous studies.
Finally, the model has been compared with the ground based ultraviolet mea-
surements of Lubin et al. (1989). Calculations excluding the effects of scattering
cannot explain these measurements, inferring a total ozone abundance which is
much lower than was observed. On the other hand, the calculated irradiance ratio
including multiple scattering agrees well with observations. The total ozone column
inferred from these calculations compare well with the TOMS observations except
at very high solar zenith angles where the accuracy of the TOMS version 5 dataset
may be questioned.
In conclusion, these studies provide a very satisfactory validation of a powerful
radiative transfer model for use in photochemical models. In particular, the treat-
ment of diffuse radiation at wavelengths below 310 nm, and the inclusion of mul-
tiple scattering up to solar zenith angles of 96” are both extremely important com-
ponents of the photoche~~al model.
Acknowledgements
D. Lary thanks SERC for a studentship, and H. K. Roscoe for many helpful discus-
sions. The authors would like to thank the Geophysical Data Facility for granting
access to its database. This work was supported by a CEC grant under STEP0013
for DGXII. This work forms part of the NERC U.K. Universities Global Atmos-
pheric Modelling Programme.
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406 D. J. LARY AND J. A. PYLE
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