2se basic
the milk
1-month,
tion, and
inted out
g deposi-
»ly an ar-
» pasture
2 a need
n models
5. levels
‘en values
ilar time
ire level,”
of stronken from
, level of
nt largely
nillicuries
ture areas
ygram per
expressed
month.
strontium
on of pascuries per
ition sche-
samples are derived from an averaging procedure over a large area and should be influenced by changes in average rate factors over
that same area. In particular, we may make
the assumption that the net rate of loss of foliar-deposited strontium 90 by washoff and
grazing depletion 1s proportional to the amount
of the radionuclide present on the foliage at
any particular time. This means that during
times when the foliage is highly contaminated
more strontium 90 is lost. This assumption is
consistent with the large drops observed in milk
values following the spring peaks. Thatis, the
quick buildup in strontium 90 is followed by an
even more rapid plungereflecting the increased
amount available on the leaf for washoff.
From the preceding, the rate of change equation for the amount of strontium 90 in the plant,
exclusive of that contributed by the soil, may be
written
dL(t)
_
He PID MA)
[1]
where P(t) is the deposition rate at time 4,
L(t) the pasture level, and A the depletion
constant. The deposition rates expressed in
millicuries per square mile have been measured
by the Atomic Energy Commission and are
taken from the Health and Safety Laboratory
report (4). In conformity with Knapp, deposition rates for Tulsa were used for St. Louis,
West Los Angeles for Sacramento, and Pittsburgh for Cincinnati. Solving equation 1, then
gives
Lit)=Cje™+e-™J éD(t)dt
[2]
ire. This,
. that milk
where (, is an appropriate constant and uptake
from soil has yet. to be considered.
Uptake from soil during any month is regarded as proportional to the amount present
in the soil during that month. Soil measurements are available but their inherent variability seems to preclude any definitive quantitative specification. Knapp has presented national average soil levels of strontium 90. He
showsthat soil levels increased fairly slowly and
uniformly over the 3-year period May 1957 to
August 1960. Weshall assume that local soil
levels are proportional to the national average
soil levels. This assumption is substantiated
lth Reports
Vol. 77, No. 12, December 1962
sling from
represents
‘ht prevail
le, but not
iid not exo have an
“ontium 90
as. Thus,
In making
actors will
from farm
further by observing from figure 2 that local
deposition rates are proportional to national
deposition rates.
Thus, equation 2 for the
amount present in the pasture may be extended
to
L(t)=Cye™-+e-™{MD(jdt+C,S(t) [31
where S(¢) represents the level in the soil at
time ¢.
The depletion constant 4, which is a measure
of the rate of strontium 90 loss from the pasture, is unknown and must be estimated from
the data. It is more convenient to work with
0,693/A which is the half-residence time in the
pasture. An upper bound for this valueis the
radioactive half-life of strontium 90, which is
about 28 years. Values ranging for 14 month to
28 years were tried using a computer. Best
results were obtained for residence times between 14 month and 2 months.
One might expect that rainfall would be a
factor influencing the milk level, but trials of
models using rainfall weighted by the strontium 90 inventory instead of deposition rates
were unsatisfactory. The rate of major concern is that of deposition on the pasture. Climatic changes will reflect themselves as changes
in these deposition rates. Therefore, D(¢) in
equation 8 was replaced by a term proportional
to monthly rainfall and stratospheric inventory
of strontium 90.
Strontium 90 Levels in Barn Feed
While the cattle are in the barn during the
winter months they are using feed which was
probably obtained during the previous harvest
season. Thus, the strontium 90 levels in milk
when a majority of the cattle were in the barn
should reflect the pasture levels during the previous harvest season. This would be true only
if the cows in the milkshed, as a whole, incorporated amounts of strontium 90 into their milk
in direct proportion to the levels in the feed
they were using. To establish this assertion, an
observed ratio is defined as the ratio of stron-
tium 90 in the milk to the strontium 90 in the
feed, that is:
puc/kg. of Sr® in milk [4]
Observed ratio= auc/kg. of Sr in feed
1057