Estimation of Crown Closure through Line Sampling

Abstract

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 l_j 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 s_j. Then, its expectation is: E(l_j)=Ls_j /T. This holds true for the N trees: E(Σ^N_j=1l_j)=LΣ^N_j=1s_j /T. Dividing L into the sum of expectations of l_j (L≠0), we obtain: E(Σ^N_j=1l_j) /L=Σ^N_j=1s_j /T. Σ^N_j=1l_j /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 l_j, otherwise zero. Then, its expectation is: E(φ_j)=s_j /T. This holds true for the N trees: E(Σ^N_j=1φ_j)=Σ^N_j=1s_j /T. Σ^N_j=1φ_j is also an unbiased estimator of crown closure.