WCP 86, A preliminary cloudless standard atmosphere for radiation computation
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- 27 -
Each of the six tropospheric aerosol models may
be matched with each of the two suggested stratospheric
aerosol models - the Unperturbed and the Volcanic, depending
on the conditions to be modelled.
The unperturbed or Background Stratospheric Aero-
sol (BSA) extends between 12 and 30 km, with a total optical
depth of 0.0047. The extinction coefficient is constant
between 12 and 20 km, namely, 2.18 x Ю~ km" . Above
20 km, the extinction coefficient decreases linearly in
altitude to 3.32 x Ю~
5
km"
1
.
The Volcanic Stratospheric Aerosol (VSA) is distri-
buted in height in a manner similar to that in the unper-
turbed case. The extinction coefficient is constant between
12 and 20 km and decays linearly with height between 20 and
-
5 - i
30 km to a value at 30 km of 3.2 x 10 km . The value of
the constant extinction coefficient between 12 and 20 km,
as well as that of the total optical depth depends on the
stage of volcanic activity.
The top-most layer of the atmosphere is occupied
by the last aerosol-type, the Upper Atmospheric Aerosol
(UAA),
which has the same composition as the unperturbed
stratospheric and the aged volcanic aerosol (75%
H
2
S0
4
).
2.6 Application of the aerosol models
Profile I (URB) should be applied to all major
settled and industrial areas on the continents as well as
over oceanic areas close to Eastern coasts of continents.
Profile II (CONT I) should be applied to all other conti-
nental areas, except for deserts. Profile III (MAR I) is
to be applied over all oceanic areas except for the low
latitude Northern Atlantic Ocean during spring, summer and
fall,
when that area is usually overlain by an aerosol
of Profile V (MAR II). The desert areas of the world,
especially during Spring and summer, are often overlain
by Profile IV (CONT II).
When volcanic outbreaks are recent, within a time
span (t) less than one year, the optical depth is О.З
and consequently the extinction coefficient at 20 km is
0.0231
km"*
1
and the aerosol is of the VSA-type. When one
models a time span of one to five years since an eruption,
the optical depth is 0.1, the extinction coefficient,
28 -
_
з - l
о
е
at 20 km, is 7.7x10 km and the material is of the
BSA-type.
When the time since eruption is longer than
5 years, up to 30, the optical depth is 0.05, the extinction
coefficient, a
,
is
3.8хЮ~
km"" at 20 km, the material
BSA-type.
It snould be again emphasized that the "Volcanic
Aerosol (Aeh)"-type is supposed to model an ash-type material
and is therefore to be used only during the initial first few
weeks of a volcanic eruption.
The models do not take into account any dependence
on atmospheric humidity. They reflect therefore the situation
for relative humidity smaller than about 70%. Users who are
interested in more humid conditions are referred to the work
of Hanel and Bullrich
(1978),
Hanel
(1976),
or Shettle and
Fenn (1979) .
If the aerosol vertical profiles are used in models
in which pressure is the vertical coordinate, care must
be taken in adapting the extinction coefficient to the
pressure scale. If, with H being the scale height of the
atmosphere and H
D
the scale height of the aerosol,
-Z/H
a (z) = а (о) e
e e
and
z/H
p = P e
о
о (p) becomes
e
о
(p) = о (p
)
(-£-)
D
e ^ e ^o p
In models where the geometrical depth of the layers
varies in time (e.g.
G.C.M.'s),
the optical depth becomes
locally variable if the aerosol models are tied to fixed
pressure levels.
- 29 -
3. VERTICAL DISTRIBUTION OF RADIATIVELY ACTIVE TRACE GASES
3.1 General
There is a rapid development in the determination
of trace gas distributions and their geographical as well as
seasonal variability. For the purpose of this report it is,
however, not necessary to describe the whole scale of already
known variability (see e.e. WMO,
1981),
but to present a
single distribution for each gas, with the exception of
ozone for which three distributions are presented.
Sometimes it is advantageous to present gas mixing
ratios by analytical expressions. Whenever applicable there-
fore the formula
(3.1)
ф. (z.)
= ф.
(z.)
exp -
i 2 x l
H
was used to describe the vertical gas distribution.
Here the following symbols are used:
ф. volume fraction of substance i
z height in km
h.
average scale height for volume fraction
(volume mixing ratio) of substance i between
z and z (not to be confused with atmospheric
scale height H).
It must be stressed, however, that formula (3.1)
does not imply that the density of the gas which is responsible
for absorption and emission processes follows the exponential
law (see section
4).
Formula (3.1) is simply a recommended
interpolation formula for the volume fraction.
Trace gas densities are sometimes presented as
molecules per m
3
. In this case volume fractions can be
computed by dividing the number density of the trace gas by
the number density of the atmosphere:
(3.2) n
a
= p/kT (m~
3
)
(p in Pa, к = 1.33066 JK"
1
, T in
K)
.
- 30 -
3.2 Ozone
A variety of standard ozone profiles for different
total amounts of ozone have been proposed for the inversion
of Umkehr observations (Mateer et al.
1980).
Two of these
profiles and one standard profile for middle latitudes are
adopted for the purpose of this report. The ozone profiles
are originally presented in ozone amounts (atm - cm) per
layer. These layers are defined in pressure steps of
(3.3)
p
±
+
1
= P.//2, i = 0, 1, 34
p e Ю13.25 hPa
In order to fit these data into the scheme of
Tables 1.1 - 1.3 of this report, ozone densities have been
derived from these data by the following procedure: first
the mean ozone densities have been computed for the given
layers and plotted versus the mean height of each layer,
determined by linear interpolation from the tropical, stan-
dard and 60°N January model atmospheres (USAF,
1976).
These points have then been connected by a smooth curve
at which the densities were read off for each kilometer
altitude. Some data useful for the necessary conversions are
compiled in Table 3.1. The three recommended ozone profiles
are listed in Table 3.2. The high latitude and tropical
ozone profiles have been selected in accordance with the
zonal seasonal averages of total ozone given by London et
al.
(1976).
The relevant values are 0.38 cm STP ozone at
60°N in January (0.31 cm STP at 60°S in July) and 0.24 cm
STP at the equator for all seasons. For the purpose of this
report the slightly higher value of 0.4 cm STP is adopted
for 60° latitude. New upper atmospheric ozone mixing ratio
data are presently inferred from the Solar Mesosphere
Explorer measurements (Barth et al., Rusch et al., Thomas
et al., 1983) which also show the variability at that alti-
tude.
It seems, however, to be too early to consider these
data in the "Standard Atmospheres".
- 31 -
Table
3.1:
Conversion
of
ozone units
The molar volume
V
л
of
ozone
is not
well established.
D'Ans
and Lax
(1949) report
a
value
of
m,0
3
(1)
V
л
=
0.0216
т
3
то1
_1
(273.15
К,
Ю12.25
hPa)
m
,0,
while
the
Handbook
of
Chemistry
and
Physics (1946) states
a
density
of 2.144 g/1 at
20°C related
to water
at 4°C
which results
in an
even smaller molar volume
if
reduced
to 0°C.
Therefore often
the molar volume
of an
ideal
gas
(2)
V »
O.022414 m
3
mol"
1
(273.15
K,
1013.25
hPa)
m
is used.
The
molar mass
of
ozone
is
(3)
M
Q
«
0.048
kg
mol"
1
.
Using
V
instead
of V 1
atm-cm represents
a
mass area density
of
(4)
0.01 m •
0.048
kg
mol"
l
/0.022414 m
3
mol"
1
=
0.021415
kg m"
2
(STP)
m* atm-cm
in a
layer
of Az m
depth
is
equivalent
to an
ozone density
p of
p
« m*
(atm-cm)
•
0.021415
(kg m
atm-cm
)/Az(m)
°3
3
~3 Ш
or vice versa
(p in kg m , uz in m, m* in
atm-cm)
°3
(5)
ro* »
46.696
p
Q
Az
The weight
of 1
ozone molecule
is
(6)
0.048
(kg/mol)
/6.022-10
23
(molec./mol)
=
7.9707-Ю"
26
(kg/molec.)
2
2
If there
is 1 kg 0
3
in a
column
of 1 m
cross section
(or 0.1 g per cm ),
there
are
consequently
1.255-10
25
molecules/kg
m
2
in the
path. This implies according
to
equation
(4)
that
1 atm-cm represents
0.021415
(kg m"
2
) •
1.255-10
25
(molec.
kg"
1
) s=
2.637-10
23
molec.
m"
2
or
(and
this relation
is
independent
of the
gas):
19 2
(7)
1
atm-cm
is
equivalent
to
2.687-10
molecules/cm
.
The absorption coefficients
-1 2
a
=
absorption coefficient
per
unit mass
in kg m
a
«
molecular absorption coefficient
in m
a
s
absorption coefficient
per cm STP in
(atm-cm)~
8
_i
a
■
volume
or
linear absorption coefficient
in cm
are related
by
(compare
eqs. (4) and (5), 6 =
optical
depth):
(8)
6„ = a m* = a
0.021415
m* = a
2.687-10
23
m* = a,
■
Q13
;
2
^
0
^
K)
1C
m*
0
3
s О m on О 1 p(hPa) 273.15 0
3
P p T The last relation results from Az = m*-^ = m* —- • P pT
0
- 32 -
Table 3.2: Standard ozone density profiles for a Tropical (T), 45°N Mid Latitude (S) and
60°N January High Latitude (P) Atmosphere*. Model in wg m"
3
.
Height
km
T
S
P
Height
kin
T
S
P
О
29
57
56
30
280
220
147
1 23
54
57
31
256
197
133
2
27
52
53 32
231
175
120
3
26
50 60
33
207
154
107
4
25 50 64 34
133
145
95
5
24
50 70
35 159 121
34
6
23
51
77
36
135
Ю4
73
7
22
54 93 37
111 87
63
3
21
53
126 33 87 74
53
9
20
63 174
39 66 60
44
10
19
33 244
40
52 43
35
11 18
110
307
41 41
33
27
12
17
130
310
42
33
31
21
13
16
150 320
43
26 25
16
14 15
170
358 44 21 20
12.5
15
16
190
396
45
16.
5 16
9.5
16
24
220 435
46
13.
0
13
7.2
17
41
260
472 47
10.
5 10
5.5
13 66
300
493 43
8.
3
8.
1
4.4
19
107
340
434
49
6.
5
6.
6
3.2
20
150 ЗЗО 461
50 5.
2
4.
7
2.5
21
195
410
421
60
0. ,5 0.
5
0.17
22 233
410
379
70
0.
OS
0.
,05
O.018
23
230
400
331
30 0,
005
0. 005
0.002
24
312
3GO
236
90
0.
,0005
O. ,0005
О.ОООЗ
25
334
360
242
100
0.
,00005 0, 00005
0.00005
26 343
335 216
27
333
ЗЮ
230
195
178
total»)
g
m *
5. ,3635
7.
5626
23
32T~
ЗЮ
230
195
178
total»)
g
m *
5. ,3635
7.
5626
8.5710
29 303
250
161
atm-cm
250.
5
353.
2 400.2
total amount of Ozone determined by linear interpolation.
- 33 -
3.3 Carbon Dioxide
C0
2
is continuously measured at the surface at four
NOAA Stations (Mauna Lia, Barrow, Samoa, South
Pole).
Flask
samples are taken at 20 additional stations (Bodhaine and
Harris,
1982).
Unfortunately results are presented in two
different scales (Scripps STO 1959 and WMO 1974) which
deviate by about 4 ppmv (WMO scale gives higher
values).
For
1978 the mean values for Mauna Loa are 331 and 335 ppmv
respectively, for Barrow 335 in both scales (Mendonca,
1979).
The mean of eight flask samplings expressed in the SIO
1959 scale is 332 ppmv. For the purpose of this report 335
ppmv are adopted for 1978 and 340 ppmv for 1981. The average
increase rate is 1.4 ppmv per year. This leads to a volume
fraction of about 345 ppmv in 1985/86.
Measurements in the troposphere and stratosphere
have been reported by Jost (1971) and Bischof et al.
(1980).
The measurements (in 1979) indicate a drop in concentration
above the tropopause from about 332 ppmv to 325.5 ppmv. For
the early summer conditions during which the measurements
have been performed, low values down to
32 5
ppmv have,
however, also been observed in the lower troposphere. Since
there is an annual amplitude of ± 7 ppmv in Barrow with
minimum in late summer, the low tropospheric values may be
biased by the annual wave, and will be neglected in this
report. For the troposphere consequently a constant mean
mixing ratio equal to the values observed at the surface
(Mendonca, 1979) is adopted. In the stratosphere experimental
data published by WMO (1981) indicate a decrease in mixing
ratio of 0.5 ppmv/km between 11 and 50 km. This trend needs
confirmation and is therefore assumed to be smaller for
the purpose of this report. Also an increase of C0
2
mixing
ratio has been reported by one group (Mauersberger and
Finsted, 1980) with daytime values of 310 ppm at 25 km up
to 350 ppm at 40 km with unexplained high values at night
in the lower stratosphere (up to 400
ppm).
The recommended CO
distribution is presented in Table 3.3.
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- 35 -
3.4 Methane
For methane now a latitude dependence as well as
small seasonal variations have been detected (WMO,
1981).
This is not reflected in the model presented here. Based
upon measurements made by Ehhalt
(1974),
Fabian et al.
(1979) and Fabian et al. (1980) a distribution is adopted,
which can be expressed by (z is the altitude in km):
1.7 ppmv for z < 14 km
ф^
и
=^1.7 exp {(14-z)/19.16} ppmv, 14 km<z<55 km
0.2 ppmv for z > 55 km
сн
4
Ghazi (1984) reports slightly higher values at
higher levels, up to 0.9 ppmv between 40 and 50 km.
According to Seiler (private communication) the
CH4 mixing ratio increases at a rate of
0.026
x10"
6
per
year. Rasmussen et al. (1981) infer an increase of about
1.7% per year (0.029 x
10""
6
) .
In table 3.3 an intermediate
number was chosen. Tfie resulting methane volume fraction is
given in Table 3.3 (after section 3.3).
3.5 Nitrous Oxide
The mixing ratio at the surface in 1981 was about
303 ppt with a growth rate of 0.9 ppt per year. Extrapolated
to 1985/86 the decrease of the N
2
0 volume fraction with
height at 45°N can be described by
r
Vo - <i
2
307 ppbv for z
<_
1 6
km
307 exp
{
12 77
> ppbv for
1 6
< z
<.
28 km
9ft — 7
I 130 exp
{
. g
8
} ppbv for z > 28 km
The height z is measured in km. The formula is based
upon measurements reported in WMO (1981) taking for the
troposphere the value reported by De Luisi
(1981).
Between
the Geophysical Monitoring for Climate Change Report N0.8
(Herbert, 1980) and Report No.9 (De Luisi,
1981)
the mixing
ratio of N
2
0 at the surface was corrected from values around
330 ppbv to values of 301.1 ppbv in the northern hemisphere on
the basis of a more reliable calibration. The average growth
rate was determined to be 0.82 ppbv yr"
1
from 1978-1980. It
was 1.5 ppbv yr
-1
for the period 1977-1981 with an excessive
value of 3.7 in Samoa (~ 1%
yr""
1
).
Excluding the Samoa value
the growth rate would be 0.9 ppbv yr"
1
. The resulting N
2
0 volume
fraction is also given in Table 3.3 (after Section 3.3).
- 36 -
3.6 Carbon Monoxide
In the troposphere the CO concentration is highly
variable with geographical latitude (> 0.25 ppmv at 70°N,
0.06 ppmv south of
40°S).
Because of the small radiative
effect of CO it seems, however, to be sufficient to use a
single distribution. We adopt a mixture between Junge's
"North Atlantic" model (Junge, 1971; Warneck et al., 1973)
and more recent measurements by Fabian et al.
(1980),
Farmer
et al.
(1980),
Ehhalt et al. (1975 a,
1978),
Volz et al.
(1981),
During the second flight of Space Shuttle CO was mapped by
means of the OSTA-1 experiment (Reichle et al.,
1982).
Signi-
ficant gradients of the middle tropospheric CO were detected
in both, latitude and longitude. The mixing ratios range
between 80 and 190 ppb. There seems to be a tendency that
the higher values build up in the northern hemisphere east
of continental coasts. The resulting CO volume fraction is
given in Table 3.3 (after Section 3.3). The tropospheric values
tend to be representative for north hemispheric conditions over
continents.
3.7
Nitric Acid
The
HN0
3
distribution i
s
not very well known and
seems in certain altitudes to be variable by a factor up to
10.
The distribution adopted here is based upon spectro-
scopic measurements made by Murcray et al.
(1974),
Lazrus
and Gandrud
(1974),
Harries (1974) and Fried and Weinman
(1970).
The vertical distribution can be approximated by
Ф
HN0-
r
I 0.1 ppmv
n
f
z - 22.
ex
P { 2.9 * PP
mv
= ^s
6 ppmv
25 - z
6 exp {
5 б
} ppmv
1 feXp {
3
2 ~
2
Z}
PP
11
^
for z < 10 km
for 10 < z < 22 km
for 22 < z < 25 km
for 25 < z < 35 km
for z > 35 km
The resulting volume fraction is given in Table 3.3 (after
Section 3.3).
Ghazi (1984) reports values between 5 and 12 ppbv at
23 km height,
8.6-12.4
at 25 km and 2.6-3.9 at 30 km. Then,
however, the volume fraction drops to
1.1-1.9
at 33 km and to
0.5 at 35 km, slightly quicker than assumed in Tables 3.3 and 3.4