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 (1956) for elliptical-shaped cross-sections; minimum error in area estimation was obtained by using the geometric mean of the maximum diameter (major axis) and the diameter at right angles to the maximum diameter (minor axis). Quantitative estimates of the errors to be expected when using stem analysis computation algorithms have been infrequently reported in the scientific literature. Consequently, users must assume that estimation error is minimal. However, the results of this study demonstrate that the degree of estimation error varies substantially depending on the sampling strategy used; 95% prediction limits (minimum/maximum) for relative error ranged from a minimum of -9.19%/5.85% to a maximum of -34.10%/42.19%. Although the results obtained in this study are specific to the computation algorithm used and the sampling strategies considered, they nevertheless demonstrate the importance of evaluating the accuracy of growth estimates derived from stem analysis. This evaluation step is particularly critical when using results obtained from stem analysis in assessing responses to extraneous factors that generate significant but minimal growth responses. Although the results of this study are consistent with those reported in the literature, further assessment of other sampling strategies, outside of the range commonly used in forest research, maybe warranted in future evaluations. In summary, given the variability in the accuracy of the growth estimates obtained from the various sampling designs assessed in this study, determining the precision of estimates derived from stem analysis algorithms under a given sampling strategy should be considered an essential prerequisite when using the stem analysis approach.