0
p-2y-y —~ (A; # A)n; = 0
for i>1
(2)
» we introduce the following
ions:
= HE, where F, is the exhalation
1 Rn™ atoms from the ground
This condition means that the
Rn™ and Rn™ in a vertical air
to the exhalation rate of its
ea.
°t > 1. This condition reflects
n of newly formed Po™ or Po™*
air and their deposition on the
= 0 for: > 1. This takes into
that all atoms and carrier par’ products reaching the ground
mn will be deposited.
)7 0 fori=1,2,3...,
a& consequence of radioactive
coefficient K is quite variable
rding to the vertical variations
ad atmospheric stability. Some
layers can be distinguished
slope of the function K (z). In
or near the earth’s surface K
with altitude, following an
ear or power law of z. Apdient wind height, dK/dz dees nearly independent of altir troposphere under normal
to the high stability of the
gain decreases rapidly above
nd is likely to approach a
lue in the lower stratosphere.
and velocity and temperature
—_
Oo
oS
—_
o
=
—
AVN
3801
10°
Turbulent diffusion coefficient K(cm?/s)
—
aan aRa empoBesa dreerie
ae pemimetnbsa ealina or aeemai
dn
c tn)
cpeeettmme mab eur
sumptions the equilibrium vertin™, Rn™, and their decay produined from the following system
uations:
INTERNATIONAL SYMPOSIUM ON TRACE GASES AND RADIOACTIVITY
al * +m
: the same removal rate ean be
ee
hort-lived Rn™ decay products
eay products A, >> A,. For Pb®™°
Icm
10cm
Im
10m
100m
1km
km
30km
Altitude
Fig. 1.
Vertical profiles of the turbulent diffusion coefficient.
profiles with time result in fluctuation of K by
about 2 or 3 orders of magnitude in the ground
layer and by about 1 or 2 orders of magnitude
in the upper troposphere. The influence of these
uncertainties on the vertical distribution of the
natural radionuclides was estimated from solutions of (2) for twenty different K profiles.
These profiles cover the total range of fluctuation of the turbulent diffusion coefficient that
seems to be possible according to the diffusion
diagram given by Lettau [1951].
Five characteristic K profiles which correspond to typical conditions of turbulence in the
troposphere are shown in Figure 1. The K pro-
rapid decrease of the turbulent diffusion coeffi-
clent was assumed in the tropopause region approaching a constant value of K = 3 x 10* em’/
sec between 20 and 30 km. In either case the gas
kanetic diffusion coefficient, which is about 0.05
em’/sec for Rn™ and Rn™ atoms, can be neglected,
NUMERICAL TREATMENT
We use the abbreviations
r,*
file SSN is an exampleof strong vertical mixing,
Putting
weak vertical mixing throughout the lower
troposphere. For JWN,diffusion in the ground
layer was assumed to be very weak, which is
, = mh,
and the profile WNN is an example of rather
typical for a strong inversion near ground. The
profile NNN is likely to be representative of
normal turbulence conditions throughout the
troposphere. In all these five typical cases a
Ay
for
=A, tA
v=
for
1
vp > 1
i-l
¢g, = apt
, , Ag yy
ve}
and defining a,,, recursively by
Oia»
=
r,*
A,
_
2~> 1
r,* Or ysl
¥ = lye eryut —
We
e- ° we
~
(3)
yoo.
an
Los
:
1
(4)