data. Unfortunately, these results were derived
by using data from only 2 months in the entire
sampling period, even though the 2 monthsselected seem to be particularly significant.
Critics have pointed out that the estimates for
a, and @, which turned out to be 0.11 and 2.4
respectively, vary quite widely according to the
particular 2 months picked for solution. In any
case, 1f one has feelings, subjective or otherwise,
about the relative effects of different months,
country.
Harris and co-workers (2) have introduced
an empirical model for short-lived radionuclides
which includes the effects of barn feeding. In
predicting future milk levels, Kulp (3) has
used the same general model as Knapp with
different time periods. In his formulation 2,
refers to the cumulative deposit of strontium 90
measured at the midpoint of the growing season
and w, is the average rate of deposition per 6
monthsof a particular growing season. In this
case, only 5 years of data yielding five points
can be used to estimate the 2 parameters a, and
a, Thus, it is not surprising that a predicted
level should agree with an observed level no
matter what the true relationship or estimation
procedure should happen to be. In fact, in-
creasing the number of parameters to 5 would
lead to a perfect fit regardless of the input vari-
tifact due to letting the cows out to pasture
before the second peak.
The preceding statements indicate a need
for developing meaningful prediction models
which apply not only to average U.S. levels
over a yearly period but to specific area values
which may prevail during particular time
periods.
Strontium 90 Levels in Pasture Feed
Considerfirst the concept of “pasture level,”
which is defined as the concentration of stron-
tium 90 per kilogram of dry feed taken from
that pasture by grazing. This net level of
strontium 90 in the pasture is dependent largely
on the following factors:
1. Rate of deposition expressed in millicuries
per square mile per month.
2. Net rate of gain from other pasture areas
expressed in micromicrocuries per kilogram per
menth.
3. Net rate of absorption from soil expressed
in micromicrocuries per kilogram per month.
4, Net rate of loss by washingoff of strontium
90 particulates and grazing depletion of pasture grasses expressed in micromicrocuries per
kilogram per month.
We mayrepresent the pasture condition schematically as in figure 1.
“
pie28
Lf WASHOFF
a.
os ane
GRAZING DEPLETION
= RU YY
, &
AAMAL/ADIA x
Y
,
1,
oy» t ij
5 dat
PASTURE
Ayrndd,
ones
x
2
ett
DONQ ae:
Fe
ae +‘
weighted least squares is the appropriate estimation technique. Knapp’s figures are about
30 percent too low during a period of about 9
months (October 1959 to July 1960), an
anomaly which he attributes to winter barn
feeding of cows in northern areas of the
ables. If one looks critically at these basic
models, one is inclined to wonder why the milk
levels should be related to the previous 1-month,
6-month, or any other period of deposition, and
if so, why linearly. Harris (2) has pointed out
that the apparent lag time from spring deposition peaks to milk level peaks is probably an ar-
Figure 1.
1056
Schematic representation of strontium
90 movement
The milk level is the result of sampling from
the dairies in the milkshed and represents
average transport factors which might prevail
over a large numberof farmsas a whole, butnot
on any farm in particular. We would not expect as large an area as a county to have an
appreciable net gain or netloss of strontium 90
particulates from other pasture areas. Thus.
this factor is neglected in figure 1. In making
computations average gain andloss factors will
be used which will undoubtedly vary from farm
to farm or from pasture to pasture. This.
again, is justified by the observation that milk
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