Canopy probabilistic reconstruction inferred from Monte Carlo point-intercept leaf sampling

The usefulness of a probabilistic technique to describe 3D foliage geometrical traits depends on the possibility of quickly and cheaply collecting a leaf data sample. The present simulation study was designed to provide the statistical information necessary to drive and control a foliage random sampling process on a real tree canopy (considered as a population of leaves) and to evaluate two corresponding statistical reconstruction outputs. A point-intercept leaf collection method was simulated on a single walnut-tree crown (7.20 m2 surface area) by performing a Monte Carlo (MC) sampling from a data set obtained by digitising all 1558 leaves. Random (R) and adaptive Kernel (aK) methods were employed for foliage synthesis. Thirty canopies reconstructed from the same MC data sample (describing 250 leaves, i.e. less than 20% of crown leaf number) by both procedures indicated that the variability associated with each simulation process can be neglected, i.e. MC leaf sampling played the principle role in driving foliage reconstruction and deciding canopy geometrical traits. A crucial point of the procedure was to define a method to construct confidence envelopes for the artificial geometrical canopy parameters, given that for practical concerns in the field there is a need to sample the real canopy only once: 30 independent samples (describing 250-300 leaves) were generated by resampling with replacement (bootstrapping) one extracted leaf data sample (describing 300 leaves) and the corresponding canopies were simulated. The reconstructed canopies were characterised from a structural perspective in terms of foliage surface area, vertical leaf area density, single leaf area, and leaf angles. The synthesised canopies were evaluated from a functional perspective in terms of sunlit surface area projected orthogonal to sunbeam direction (silhouettes), and sky vault-integrated silhouette to (canopy) area ratio (STARSKY). The virtual walnut-tree foliage reproduced by electromagnetic digitising was the reference to corroborate all corresponding reconstructed canopies. The aK method appeared more accurate and precise than the corresponding R technique to represent real foliage geometrical traits. In general, the proposed aK statistical canopy reconstruction method appears to be promising to infer the geometrical features of a broad-leaf tree crown from a foliage sub-set, even if its applicability depends on the size of the considered tree, i.e. on the practicability of collecting a leaf data sample.