I proposed two new theoretical methods for estimating the crown closure through line sampling. These are an application of Masuyama's method for estimating an area based on a line sampling unit, using integral geometry. The first method is as follows: First, we establish a sample line of fixed length
L in the stand, on the assumption that the crown projection area of all trees is included in an area of the stand
T. Next, we define a continuous variable
lj which takes the value of that part of the length of the sample line which is included within the crown projection area of the
j-th trees
sj. Then, its expectation is: E(
lj)=
Lsj /
T. This holds true for the
N trees: E(Σ
Nj=1lj)=
LΣ
Nj=1sj /
T. Dividing
L into the sum of expectations of
lj (
L≠0), we obtain: E(Σ
Nj=1lj) /
L=Σ
Nj=1sj /
T. Σ
Nj=1lj /
L is an unbiased estimator of crown closure. The second method is as follows: A sample line is established as in the first method, and a uniform random number is selected within the length of the line
L. Next, a discrete variable φ
j is defined which takes the value 1 if the value of the random number is smaller than
lj, otherwise zero. Then, its expectation is: E(φ
j)=
sj /
T. This holds true for the
N trees: E(Σ
Nj=1φ
j)=Σ
Nj=1sj /
T. Σ
Nj=1φ
j is also an unbiased estimator of crown closure.
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