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2.3.5. Spherically averaged silhouette to total area ratio (STAR) and woody area

Procedure

Spherically averaged silhouette area of a tree was computed with Gauss-Legendre integration as

where Streeij) is the silhouette area in direction Ωij, and i and j are the azimuth and zenith angles, respectively. For explanation of the other symbols, see Eq. (4). The STAR with foliage only was calculated as

where $S¯tree$ is the spherically averaged silhouette area of the tree including both foliage and woody parts, and TAfoliage is the total area of foliage in the tree. We also calculated the total area of woody parts for each tree, utilizing the spherically averaged silhouette area without foliage ($S¯tree,wood$) and assuming that the total woody area (TAwood) equals four times the spherically averaged silhouette area, which is true for any convex body. It was assumed that there is no self-shadowing, because the branches in the trees were sparse. Finally, STAR with woody parts included (STARall) was obtained by applying Eq. (8) but now including both woody parts and foliage in total area (i.e., replacing TAfoliage with TAall= TAfoliage+TAwood).

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