730
PELLETIER, WHIPPLE, AND WEDLICK
Another reason was that the exponential model has three terms to
manipulate whereas the linear model has only two. For a process as
complicated as the deposition of airborne radioactivity, this additional
term seemed to be an advantage.
The specific equations for the pointsin Fig. 2 are shown in Table 3.
Table 3—- EQUATIONS OF THE FORMOF EQ. 1
DETERMINED BY CURVE FITTING TO THE
DATA SHOWN IN FIG. 2
Dates
Equation
Dec. 27, 1962, to June 13, 1963
1.0 x 10° (1,065 — e-?-11r)
June 13, 1963, to Oct. 31, 1963
0.8 x 10° (1.04 ~ e717)
Oct. 31, 1963, to Dec. 26, 1963
1.4 x 108 (1.04 ~— e~% 117)
Dec. 26, 1963, to Mar. 19, 1964
Mar. 19, 1964, to June 15, 1964
(part a, Fig. 2)
(part b, Fig. 2)
(part c, Fig. 2)
The values of the parameters H, a, and b do not necessarily have
any physical significance. The best fit to the points for thefirst six
four-week periods (part a, Fig. 2) was made with b equal to 0.11. Except for the one for the daily rainfall data, all subsequent curves could
also be fitted with b equal to 0.11. However, these curves could have
been fit equally as well with smaller values of b and correspondingly
higher values of H. It appears that with values of b in the range of 0.11
we are at the threshold of being able to distinguish an exponential function from a linear one.
APPLICATION OF THE MODEL
The model used to predict the deposition of gross beta radioactivity at Tecumseh had the values of Hand a for the time periods shown
in Table 3. The results are shown in Fig. 3. The model overestimated
the measured deposition 14 times with an average overestimation of
27.8%. The model underestimated the measured deposition only 5 times
with an average underestimation of 19.2%. The computedtotal deposi-
tion for the entire 76-week period was 12% higher than the measured
total deposition. It appears that there is a systematic difference be-
tween the computed and the measured depositions. The mostlikely
explanation for this discrepancy lies in the measurement of rainfall,
which has already been mentioned. Plans have been made to compare
the collection efficiency of the 10.5-in.-diameter funnel during a fourweek collection period and of the 8-in.-diameter funnel during a weekly
collection period to the efficiency of the standard rain gauge during a
weekly collection period.