DIFFUSION IN THE UPPER ATMOSPHERE 
the basic facts of the vertical distribution of ozone, 
when incorrect meridional distributions of the total 
ozone (vertical number integral, as defined by equation 
(79)) were obtained. Molecular diffusion proved to be 
negligible; the addition of vertical eddy diffusion im- 
proved the results with regard to the meridional dis- 
tribution. However, the annual variation was still in- 
correct. Finally, the addition of vertical and horizontal 
advection due to the average general circulation in the 
lower stratosphere yielded fairly satisfactory theoretical 
values. Tables V and VI condense the findings of Dtitsch 
Taste V. MeRIDIONAL VARIATIONS or ToraL OzonE* (in cm) 
(After Dtitsch [8]) 
Latitude North 
Basis of computation Midsummer Midwinter 
25° 45° 70° 25° 45° 60° 
Direct radiation 0.52 | 0.33 | 0.28 | 0.31 | 0.17 | 0.07 
Direct + diffuse ra- 
diation 0.39 | 0.27 | 0.20 | 0.26 | 0.17 | 0.14 
Direct + diffuse ra- 
diation + vertical 
eddy diffusion 0.19 | 0.20 | 0.21 | 0.19 | 0.20 | 0.22 
Observation 0.20 | 0.24 | 0.26 | 0.19 | 0.23 | 0.26 
* Under the assumption of equilibrium in vertical columns. 
and may be regarded as proving the influence of terms 
like n,C,-k and the horizontal components of V- V in 
equation (96). 
301 
Other studies based on all the terms of equations (96) 
and (97) do not exist. The main reason is the lack of 
appropriate observations of gas concentration, including 
moisture, in the upper atmosphere. Particulate matter 
and its diffusion appear to be more easily observable. 
As an example of dust transportation, a paper by 
Brandtner [8] may be mentioned. On March 29, 1947, 
dust from North Africa (latitude 32-385°N, longitude 
0-3°E), which was brought into the upper troposphere 
by the passage of two cold fronts, was transported with 
south-southwesterly winds and arrived approximately 
15 hours later at latitude 50° in western and central 
Europe. Brandtner’s study of the upper-air weather 
maps proved that the rising of the dust was due to 
horizontal convergence, the settling to divergence of 
the wind. 
Another example is the eruption of Krakatoa on 
August 26-27, 1883. The extremely violent catastrophe 
and the attendant optical phenomena commanded gen- 
eral attention in all parts of the world. Reports like 
those of Kiessling [19] and Symons [87] offer excellent 
bases for future studies of atmospheric diffusion. 
Great masses of fine volcanic dust were ejected to levels 
of more than 30 km. Floating with the currents in the strato- 
sphere, the haze caused extraordinary twilight glows and 
Bishop’s ring around the sun. From this, the diameter of the 
average particle was deduced to be 0.1 X 10-*—0.4 X 107 
TaBie VI. ANNUAL VARIATIONS OF TOTAL OZONE AT 60°N (in em) 
(After Diitsch [8]) 
Month 
Basis of computation 
I II oat IV V vI Vil | vir) Ix x XI XII 
Direct + diffuse radiation + vertical eddy 
diffusion (under the assumption of equi- 
librium in vertical columns)................ 0.22 | 0.22 | 0.22 | 0.22 | 0.22 ! 0.22 | 0.21 | 0.21 | 0.22 | 0.22 | 0.22 | 0.22 
Direct + diffuse radiation + vertical eddy 
diffusion + average horizontal and vertical 
circulation in the lower stratosphere...... 0.23 | 0.25 | 0.27 | 0.25 | 0.22 | 0.19 | 0.18 | 0.17 | 0.17 | 0.17 | 0.18 | 0.20 
@bsemuatromineyeess vs ctese diane sem iilinna ad 0.27 | 0.30 | 0.31 | 0.30 | 0.29 | 0.26 | 0.24 | 0.23 | 0.23 | 0.23 | 0.23 | 0.25 
Systematic differences between the last two lines of 
Table VI can be disregarded; they may be caused by 
unreliable values of physical constants in the term q“”’. 
Annual averages of the vertical ozone distribution 
show a slow increase of O;-concentration in the tropo- 
sphere and lower stratosphere when a rapid increase 
occurs a few kilometers above the tropopause. This 
appears to be due to rapidly decreasing D-values in 
these layers. Thus, another proof for the shape of the 
D-curve about 15 km above sea level, as shown in Fig. 2, 
is obtained [21]. In this connection, the observed cor- 
relation between total amount of ozone and pressure 
at sea level appears to be explained by vertical oscilla- 
tions of the tropopause and layers of dD/dz < 0 when 
the layers of g remain unchanged. 
em. The mean height of the glow stratum decreased 15 km 
fairly continuously during 5 months which is approximately 
0.1 em/see [c.f. §9]. The glow stratum travelled several times 
around the globe completing one circuit in approximately 13 
days. On the first circuit the band of twilight glows was cen- 
tered at the latitude of Krakatoa, 6°S., and the mean exten- 
sion north and south was 15°. During the secend circuit the 
limits were not so determinate. Up to Oct. 5th the rate of 
lateral expansion was maintained, but after this epoch a 
distinct retardation in the latitudinal spread of the main 
body of haze occurred. In November, a sudden rush took 
place, which by the end of this month, caused the phe- 
nomenon to be seen on the major parts of North America 
and Europe up to latitude 60°. While the material was cross- 
ing 30°N it was simply spreading north and south, and after- 
wards turned around to move from SW to NE [19]. 
