Stem tapers are mathematical functions modelling the relative decrease of diameter (rD) as the relative height (rH) increase in trees and can be successfully used in precision forest harvesting. In this paper, the diameters of the stem at various height of 202 Pinus nigra trees were fully measured by means of an optical relascope (CRITERION RD 1000) by adopting a two-steps non-destructive strategy. Data were modelled with four equations including a linear model, two polynomial functions (second and third order) and the Generalised Additive Model. Predictions were also compared with the output from the TapeR R package, an object-oriented tool implementing the β-Spline functions and widely used in the literature and scientific research. Overall, the high quality of the database was detected as the most important driver for modelling with algorithms almost equivalent each other. The use of a non-destructive sampling method allowed the full measurement of all the trees necessary to build a mathematical function properly. The results clearly highlight the ability of all the tested models to reach a high statistical significance with an adjusted-R squared higher than 0.9. A very low mean relative absolute error was also calculated with a cross validation procedure and small standard deviation were associated. Substantial differences were detected with the TapeR prediction. Indeed, the use of mixed models improved the data handling with outputs not affected by autocorrelation which is one of the main issues when measuring trees profile. The profile data violate one of the basic assumptions of modelling: the independence of sampled units (i.e., autocorrelation of measured values across the stem of a tree). Consequently, the use of simple parametric equations can only be a temporary resource before more complex built-in apps are able to allow basic users to exploit more powerful modelling techniques.

中文翻译：

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意大利中部黑松的锥度函数：是否需要更复杂的计算系统？

茎锥度是数学函数，可模拟树木中相对直径（rD）随着相对高度（rH）增大的相对减小，并且可以成功地用于精确的森林采伐中。本文采用两步无损策略，利用光学相对论仪（CRITERION RD 1000）对202棵黑松不同高度的茎径进行了全面测量。使用四个方程对数据进行建模，包括线性模型，两个多项式函数（二阶和三阶）和广义可加模型。预测也与TapeR R包的输出进行了比较，TapeR R包是实现β的面向对象工具-样条函数，广泛用于文学和科学研究。总体而言，数据库的高质量被认为是使用几乎彼此等效的算法进行建模的最重要驱动力。使用非破坏性采样方法可以完全测量正确构建数学函数所需的所有树木。结果清楚地显示了所有测试模型具有较高的统计学意义的能力，调整后的R平方高于0.9。通过交叉验证程序还计算出非常低的平均相对绝对误差，并且相关的标准偏差小。通过TapeR预测检测到实质性差异。确实，混合模型的使用改善了数据处理，其输出不受自动相关性的影响，这是测量树木轮廓时的主要问题之一。轮廓数据违反了建模的基本假设之一：采样单位的独立性（即，跨越树的茎的测量值的自相关）。因此，在更复杂的内置应用程序能够允许基本用户利用更强大的建模技术之前，使用简单的参数方程式只能是一种临时资源。