151 
lized to 
s randomly 
to index 
ed on each 
e height 
ng a pocket 
ees in 
easurements 
:15840 
are 
from 
between 
unit, was 
ery. This 
cing a 
of 
were 
(7X, 10X, 
f magnifi- 
sampling 
revent 
counted, 
ire. 
he 
s (crown 
■ as an 
following 
(2) BAp = f(CCp, HT p ) 
where CCp = estimated 1:15840 imagery average crown closure 
HTp = estimated 1:15840 imagery average tree height 
(3) CCp = f(CC i ) 
where CC^ + estimated 1:120000 imagery average crown closure 
The equation used to associate estimated ground basal area with estimated 
1:15840 imagery basal area was (Larson, Moessner, and Ffolliott, 1971): 
(4) BA g = 28.04 + 0.852(BAp) 
The equation used to estimate 1:15840 imagery basal area from average 
crown closure and average tree height measurements was (Moessner, 1964): 
(5) BAp = 55.32 - 0.838(CC p ) - 0.816(HT p ) + 0.0190 (CC p , HT p ) + 
0.00545(HTp) 2 
Linear regressions were used to quantify the unknown association between 
estimated average crown closure determined from measurements on 1:15840 
imagery and from measurements on 1:120000 imagery. Equations relating 
these two variables were defined for each data set obtained from the four 
levels of magnification. Only the equation defining the relationship with 
25X magnification is presented: 
(6) CCp = 12.84 + 0.185(0^) 
Conceptually, it was now possible to obtain the ground estimates of 
basal area that are required in the synthesis of forest stocking equations 
through substitution of variables in the regression equations which were 
used to approximate the above-mentioned mathematical relationships. 
Synthesis of Forest Stocking Equations 
The synthesis of forest stocking equations is based on the following 
mathematical procedure (Brunk, 1965): 
(a) the development of probability density functions from the basic 
source data, i.e., the ground estimates of basal area derived 
as outlined above; and 
(b) the development of cumulative distribution functions from the 
density functions. These distribution functions, by definition, 
are described as continuous from the right and, therefore, can 
be considered "exceedence functions."