OZONE IN THE ATMOSPHERE 
Mecke’s result, for which the total ozone amount and 
altitude of the maximum content are given, according 
to the original and to the revised formula, as well as 
according to Wulf and Deming’s result, valid only for 
the sun at the zenith. Below 10 km the ozone content 
approaches zero because at lower altitudes the de- 
ozonizing effect of light becomes prevalent. Above 50 
km the ozone content again approaches zero because 
the frequency of ozone-forming collisions decreases 
much more rapidly with altitude than does the oxygen 
concentration. The highly gratifying results from the 
analytic integration should not lead us to forget that 
Mecke’s theory cannot be developed further in view of 
its inherent simplifications. 
Wullf’s treatments have been independently expanded 
by Schro6er [89] and Diitsch on the basis of more modern 
theories. These make allowance first of all for the sun’s 
elevation, that is, the effect of season and latitude. The 
ozone calculation is again performed layerwise, from the 
top downward with the aid of equation (23). New data 
are used for the seasonal and zonal vertical temperature 
variation in the stratosphere, for the ozone absorption 
coefficients in the vicinity of 2100 A, for the deviations 
of oxygen absorption from Beer’s law, and for extra- 
terrestrial solar radiation. Whereas the results concern- 
ing vertical ozone distribution and total ozone amount 
are satisfactory, one finds a decrease of ozone from 
equator to pole and from summer to winter. Even if the 
effect of the daily variation of the sun’s position as well 
as of Rayleigh scattering is considered, it is not pos- 
sible to reverse this erroneous trend completely. It 
follows that the observed ozone distribution cannot be 
explained by assuming pure radiation equilibrium at 
every pomt of the atmosphere. Recently, Craig [17] 
has reached the same conclusion. 
An explanation for the seasonal variation of ozone 
solely on the basis of temperature variation [49, 98] 
is not convincing. 
Ozone under Conditions of Disequilibrium. The 
period of time required for photochemical equilibrium 
to be established was investigated quantitatively by 
Wulf [104]. Diitsch [27] gives the temporal trend of 
283 
Schroer, too, emphasizes the conclusion that (in middle 
latitudes) photoequilibrium occurs only down to about 
33 km, and that the ozone distribution below this alti- 
tude is determined by transport processes (turbulence). 
The Effect of Air Motion on Ozone. Diitsch lets the 
subscript s denote the effect of disturbances, R repre- 
sent the absolute gas constant, takes the molecular 
weight of air as 28.9, and finds the effect of air currents 
on ozone concentration to be 
() [03] os . 28. 9g (6) [03] 
Ss \- =, (% [Os] + |) 
i a AlOs] , , 910s eS ) 
Me dy 
This derivation is based on the ee assumptions 
that the air density varies only with altitude and that 
the vertical temperature gradient is zero, an assumption 
that is Justified only as applied to the lower stratosphere. 
Reed [80] therefore took the vertical temperature gra- 
dient into account and obtained the expression 
Cc =-», {103 (aa + a) + a. (28) 
0 
He uses this equation primarily in treating the diurnal 
meteorological ozone fluctuations and in establishing 
a theory concerning seasonal and zonal ozone fluctu- 
ations. Diitsch, moreover, finds the effect of turbulent 
exchange (austausch) to be 
0 a 
dz [O2])’ 
ae = [Oz] 0 {4 
OU He: p oz 
where the subscript a denotes the effect of the austausch 
and A represents the austausch coefficient. Diffusion 
may be neglected. Because of the long time required 
for establishment of photochemical equilibrium at lower 
altitudes, changes in the concentration owing to flow 
and turbulence play an essential role. If B is the change 
in ozone concentration per second caused only by air 
motion (flow and austausch) then equation (23) be- 
comes 
(27) 
(29) 
ozone concentr. enon in the case of a disturbance; during B 
the time te = + (fof;/k{M])~“, the ozone concentration fe + 20s] (30) 
is reduced to eqyonomnielialie “We of its original value, [03] = [0+] paar’ k (M1), 
corresponding to the “time of half restoration” used 5 
by Wulf. Within high altitude layers (2 35 km) cor- and the equation for disequilibrium becomes 
oa tn 4/ ay +0) P FY oat / es ael? rma 
al (t:) Seno ar (i ar F091 [02] tan an 0 
[0] = ao a (31) 
/1(6 + a0) (i + 30g) 
4/ ETDS 5, Selle <1 SY Ee ps oe 
K[M] K[0.][M] K(M] : 
rection of the disturbed equilibrium takes place almost 
immediately; between 30 and 25 km from several days 
to several months are required; at low altitudes (‘‘pro- 
tected regions”) equilibrium is practically never re- 
gained. At high elevation of the sun, equilibrium is es- 
tablished more rapidly than in the case of low sun. 
Thus, equilibrium can be established only if fp > 
B/(2[0.]); equation (31) is always valid. 
Diitsch used this expression to recompute the seasonal 
variation of ozone at various latitudes. For the layers 
above 16 km, the austausch coefficient is calculated 
on the basis of experimental results of Paneth and 
