【目的】基于非参数理论,研究构建大兴安岭兴安落叶松(Larix gmelinii)非参数可加性树干削度方程,并与传统的Max and Burkhart 参数削度方程进行对比。【方法】利用树高、胸径、不同高度处直径、不同部位高度等变量及其变形构建非参数可加性削度方程。采用 7种光滑样条函数:薄板回归样条函数(TP)、 Duchon 样条函数(DS)、三次回归样条函数(CR)、P-样条函数(PS)、高斯过程平滑样条函数(GP)、B-样条函数(BS)和局部回归光滑函数(LO),基于R软件mgcv包的Gamm函数对非参数模型进行拟合。【结果】使用相对直径(d/D)作为因变量,胸径的平方(D²)、树高(H)、相对树高的算术平方根($\sqrt{h/H}$)作为自变量, 构建兴安落叶松最佳非参数可加性树干削度方程。拟合结果表明:基于CR和LO样条函数的可加性削度方程具有较小的R²(决定系数)和较大的赤池信息量准则(AIC)值,且CR和LO的残差图重心线略呈中间高、两头低的趋势。其他基于5种光滑样条函数的可加性削度方程表现出相似的拟合结果。可加性模型除了使用LO样条函数外,其他样条函数都优于Max and Burkhart参数削度方程的拟合结果。总体检验结果表明,除了CR样条函数模型外,其他各非参数模型(TP、 DS、 PS、GP 和BS)与拟合结果基本一致,即都优于Max and Burkhart参数削度模型的预测精度。基于树干不同高度直径预测的误差对比表明,除了CR模型外,非参数模型(TP、 DS、 PS、GP 和BS)在大多数树干高度处直径预测的平均误差和绝对平均误差都小于Max and Burkhart参数模型预测值。【结论】非参数模型(TP、 DS、PS、 GP和BS)在拟合统计量、残差分布图、总体和树干不同高度处直径的预测精度都表现出一致性,并优于林业上通常使用的Max and Burkhart参数削度方程。当模型以预测为目的时,所构建的非参数可加性削度方程可用于大兴安岭兴安落叶松干形和材积预测。

【Objective】Based on the nonparametric theory, the nonparametric additive taper equation was constructed for dahurian larch (Larix gmelinii) in Greater Khingan Mountains. The common parametric taper equation of Max and Burkhart, in forestry, was used for comparison.【Method】A nonparametric additive taper equation was constructed using the total height, diameter at breast height, diameter at different heights, height at different stems, and their transformation. The nonparametric model was fitted based on the Gamm function in the mgcv library of the R software. Specifically, we used 7 smooth splines: thin plate regression splines (TP), Duchon splines (DS), cubic regression splines (CR), P-splines (PS), Gaussian process smooths (GP), B-spline (BS), and local regression (LO).【Result】The optimal nonparametric form of taper equation was constructed using response variable relative diameter (d/D) and explanatory variables such as the square of diameter at breast height (D²), total height (H) and square root of relative height($\sqrt{h/H}$). Fitting results showed that the additive taper equations based on CR and LO had smaller R² and larger AIC values, and the residual trend lines of CR and LO were slightly higher in the middle and lower at both ends. The nonparametric additive taper equation fitting effects of the other 5 smooth splines were similar. The fitting results of these additive models are better than those of Max and Burkhart, except for LO model. The overall validation results showed that the nonparametric models (TP, DS, PS, GP and BS) were basically consistent with the fitting results, except for CR. That is, they were superior to the parametric taper equation of Max and Burkhart. The error comparison based on the prediction of different height diameters of stems showed that the average error and absolute mean error of the nonparametric models (TP, DS, PS, GP and BS) were less than those of Max and Burkhart at most heights, except for CR. 【Conclusion】The nonparametric models (TP, DS, PS, GP and BS) showed consistent accuracy in fitting statistics, residual distribution, and the prediction from overall and different heights. These models are superior compared to those commonly used parametric taper equation of Max and Burkhart in forestry. When prediction is the main purpose for building a model, the nonparametric additive taper equation constructed in this study can be used not only to predict the shape of the stem but also the volume of the dahurian larch in Daxing’anling.