DIFFUSION IN THE UPPER ATMOSPHERE 
equations (83) and (84) yield the equations of ‘“‘partial 
separation” for permanent constituents: 
Vs = Vs0 EXP (-# A oe Qs a) (45) 
or, if Z=T) and g = go, 
Vs = Vs EXP (-" [ Q: iz). (46) 
0 
For convenience, a general separation factor Q, which 
is independent of the special gas, is defined as 
d 
Q ae d ae D’ 
in which d = 0.18(po/p)(T'/T»)* is the standard coeffi- 
cient of the N».-atmosphere (see Table III). We may 
also write (cf. equation (24)) 
Qs 
Os oe Qa Wi 5)” 
and Q, = 
(47) 
Q= 
(48) 
Q6. 
1 — Q0 — 6.) 
The factor Q depends on pressure, temperature, and 
turbulence as functions of height. With reference to 
[88], 0.78 < T/T) < 1.25 for 0 S z S 100 km; the 
average 7'/T) is rather close to unity. If 7/7) = 1, the 
logarithm of d increases proportionally to z. Crude values 
of D were estimated from the intensity of the atmos- 
pheric circulation and vertical thermal stratification for 
0 = z S 100 km (see Fig. 2). Equation (46) was 
applied for molecular oxygen, argon, and helium. The 
theoretical »,-variation, as shown in Fig. 2, reflects the 
Q-variation with height. 
Inasmuch as Q ~ 0, the tendency towards separation 
begins at sea level. However, when Q < 10 * and 
(22 = 21) S 10 km, all permanent constituent gases show 
that | v1 — v2 | /va S 0.01 per cent. Therefore, the 
concentration of permanent gases is practically constant 
throughout the entire troposphere where Q ~ 10 °, as 
follows from Fig. 1. 
Regener [30] showed that vo, decreases slightly in the 
stratosphere from 15 to 29 km. Lettau [21] and Diitsch 
[8] used this fact for computing A = pD between 15 and 
30 km. Because of the term 6,u;/[1 — Q(1 — 4,)], the 
percentage separation of helium should be approxi- 
mately 20 times that of molecular oxygen. However, 
helium is not a permanent constituent. The observed 
helium distribution will be explained in Section 8. When 
no helium source and sink would exist, the height 
variation of vz, should follow the dotted line in Fig. 2. 
The coefficient d increases monotonically with height; 
increasing temperature can only slightly modify this 
trend. Regions above 100 km are subject to turbulence 
caused by diurnal heating and cooling and by tidal 
effects. However, in contrast to d, the value of D is 
limited. An estimated maximum D-value is approxi- 
mately 10° cm” sec ‘ since ¢p and Xp are unlikely to 
exceed 10*-10* cm sec and 10°-10* em, respectively 
(see Fig. 1). Thus 
lim Q = 1, 
zo 
(49) 
325 
When D < 10°cm’ see ‘and (39) isused for computing d, 
1>Q>05 if z= 160 km. (50) 
1>Q>0.99 if z= 200 km (51) 
If Q = 0.99, there should result, practically, a Dalton 
atmosphere. From this point of view, the datum levels 
OXYGEN, O5 HELIUM, He 
(PERCENT (10? PERCENT 
BY VOLUME) BY VOLUME) 
ida 19.5 20 20.5 2i 5 7.5 10 12.5 
$ i | y| 
a y 
fe me He if 
80 ow ik 
-5 iy 
rE i} 
é Ze 
i} 
= 60 -\egat 1 
= Soest \“He 
KB Opts | 
ae oh 2 4 | 
) c+ | | 
= 40 ores ! 
ET Epa | 
Zoe care, 
NW con 3// 
20-\— Wes, i 
Bee] | 
ce | 
OZ= = 
10' 10' 10° 10° 10’ © 0.1 0.2 07 08 09 
d ,D (CM*/ SEC) Q ARGON, A 
(% BY VOLUME) 
Fig. 2.—The influence of the separation factor Q on the 
height variation of concentration of heavy and light permanent 
gases. Regener’s and Paneth’s observations of vo, and vz, 
(highest levels of analyses are 29 and 25 km, respectively) are 
marked by dots. Helium is not a permanent gas and therefore 
Yee = const when condition (52) is satisfied. The absolute 
values and the height variations of the eddy diffusion coef- 
ficient D will be valid for temperate latitudes since they were 
estimated from assumptions with regard to the representative 
zonal circulation in temperate latitudes and the sign of 07'/0z 
(—, 0, and + denote lapse, isothermal, and inversional stratifi- 
cation, respectively) such that strong zonal motion and/or 
lapse conditions cause large D-values when weak zonal motion 
and/or inversional stratification cause small D-values. Other 
facts giving support to the existence of layers of dD/dz < 0 
ehisve approximately 15 and 70 km are discussed in Sections 9 
and 14. 
of 12-50, 100, and 150 km as assumed by Chapman and 
Milne [5], Mitra [26], and Maris [24], respectively, 
appear to be too low, except possibly for the last one. 
Internal sources and sinks due to photochemical proc- 
esses—which also affect nitrogen above 200 km— 
impair the computation of diffusion effects in the iono- 
sphere, even though D might be neglected in compari- 
son with d. 
8. Effects of Sources and Sinks. If y = y. = 0 and 
0 < Q S 1, equation (34) describes steady height varia- 
tions of nonpermanent gases with external sources and 
sinks. A basic flow enters one boundary of the layer 
under consideration and leaves the other. A highly 
interesting special case exists when 
Yo = Yerit = — veoesnds v»/H = —Nsolsls No ‘HT 3 
(52) 
= —Nso(Cp)o- 
Then (34) reduces to 
Vs = Yo = Const. (53) 
The concentration is constant when 70/70 equals the 
negative velocity of pressure diffusion at sea level (see 
equations (17) and (41)). Petersen [29] discussed this 
