APPENDIX B.
ESTIMATING THE 239-2405, CONCENTRATION SURFACE USING GRID
.
.
239-240
.
.
Estimating the
Pu concentration surface using GRID is a two-phase
procedure.
Yu, yy),
In Phase
1
the
slope of
the surface at each data point
i = 1,2,...,n is computed where X,
(X;,
is the east-west coordinate,
Y; the north-south coordinate and y,; the 239-240Py concentration at the
point
(X;, Y¥;).
Vv
k
=
b,
O
A weighted linear trend surface of the form
+ byw,
X,
+ baw
Lik k
2 2k Yk
k
,
=
1,2,...,8
(B1)
is fit by least squares to the eight nearest data points
each data point (X55 Yes Yas where
wa
-
Nd
lk
w
Dy.
=
k
2k
(X. Y
k? 7k )
about
1
Dy
and
D,.
|
VK,
=
Equation (Bl)
-
x)
Xx
2
+
(>
Y
7
¥)
2
k
’
=
1,2
8
revere Oe
is constrained to pass through the control point (Xj5 Yy>
yz)-
The resulting set of coefficients (bg, by, bo) for each data point are used
in Phase 2 to estimate
point (grid node).
the 239-240py concentration at each grid intersection
n
.
239-240
.
A
:
In Phase 2? the estimated
Pu concentration Yo,r at each grid node
(X,., Y_) is obtained.
For the eight nearest data points about the grid
node (X,, Y,;), eight estimates of the concentration surface are obtained,
each of the form
vo
t
=
bo.
+b.
Ot
1
X
+b
toc
Qtr
?
t
=
1,2,...,8
where the eight sets of coefficients (boys bite bo,) were obtained in Phase
1.
The final estimate of the plutonium concentration at the grid node
(X., Y,) is then obtained as the distance weighted average
y c,r
=
res,
t=1
wooy
t
ot
where
/y
/%,
Woo.
t
(B2)
2
“.
>
—
(oars max
—
DL
—
2
1.1 D max
—
D
——
(B3)
Dis the distance to a sample data point from the grid node (X., Yy), and
Dmax is the distance from (X,, Yr) to the most distant of the eight data
points.
359