A stem analysis computational algorithm for estimating volume growth and its empirical evaluation under various sampling strategies

The objectives of this study were to describe and subsequently evaluate a computational stem analysis algorithm applicable to coniferous forest tree species. Specifically, the algorithm was designed to estimate annual volume growth rates given ring-width xylem sequences obtained from cross-sectional samples located at multiple stem heights. Volumetric computations were based on the following geometric assumptions: (1) the stump, tip and sections in between were treated as geometric solids of revolution resembling a cylinder, cone, and frustum of a cone, respectively; and (2) for sections in which increments were not continuous throughout, computations were based on a geometric solid of revolution resembling a cone. Furthermore, the algorithm incorporates a correction for slant-based sectional length measurements using the Pythagorean theorem and eliminates the need to predict heights for a given age by the use of a linear interpolation procedure. The algorithm was evaluated by measuring the difference between the estimated and observed annual volume growth rates derived from 53 semi-mature jack pine ( Pinus banksiana Lamb.) trees using eight systematic sampling strategies: two sample sizes (five and ten cross-sectional samples per tree) and four elliptical-based radial selection procedures (one randomly selected semiaxis per cross-section; two semiaxes consisting of the minimum and maximum semiaxes per cross-section; two semiaxes along the major axis per cross-section; and four semiaxes along the minor and major axes per cross-section). Based on the resultant prediction intervals, estimation error was minimized when sampling four semiaxes along the minor and major axes from 10 equal-distance cross-sectional samples per tree. Specifically, approximately 95% of the relative errors would fall within the −9.19 to 5.85% interval, 95% of the time. The results of this study demonstrate the importance of quantifying estimation error for a given sampling strategy when using the stem analysis approach.