基于广义加性模型的红松树干纵向木材密度模型研建

Developing a longitudinal wood density model for Pinus koraiensis stems based on generalized additive models

摘要

【目的】人工红松是东北地区重要的用材与生态树种，其树干木材密度纵向变异对木材品质筛选、生物量和碳储量估算至关重要，传统模型难以精准捕捉其纵向变化特征。本研究旨在分析红松木材密度的纵向变化规律，构建高精度预测模型，为红松材性和生物量的精准评估提供依据。【方法】以孟家岗林场 30 株红松的 402 个木材密度样本为研究对象，首先从 9 个木材密度模型中筛选出最优基础模型，在此基础上引入传统易获取的林分变量（每公顷株数、每公顷断面积、林分平均高和林分平均胸径）构建广义线性模型，并采用连续自回归误差结构 CAR（1）降低模型残差自相关。同时，基于广义加性模型（GAM）理论构建木材密度模型，并比较了 GAM 6 种光滑函数的拟合效果。最后使用十折交叉验证法比较不同模型构建方法的预测性能。【结果】（1）红松木材密度沿树干纵向呈明显的非线性变化规律，整体表现为随相对高增加“先降后升”的趋势。（2）在基础模型对比中，自建模型 Model 9 的拟合效果最佳。以 Model 9 为基础引入每公顷株数构建的广义线性模型进一步提升了模型的拟合性能，与 Model 9 相比，其调整决定系数（ R²_adj）提高了 2.4%，平均绝对误差（MAE）下降了 0.7%。（3）采用连续自回归误差结构 CAR（1）有效降低了基础和广义线性模型的残差自相关性。修正后，两个模型的 MAE 相较于修正前分别下降了 2.4%、2.5%。（4）基于三次回归样条（CR），采用胸径、胸径年平均生长量、冠幅、相对高和每公顷株数为变量构建的 GAM 表现出最优估测能力。十折交叉验证结果进一步证实 GAM 具有更高的稳健性与泛化能力，和广义线性模型相比其 R²_adj提高了 13.25%，MAE 下降了 9.54%。【结论】本研究系统构建了红松树干纵向木材密度模型，揭示了其“先降后升”的纵向变异模式。GAM 在拟合效果、预测精度及稳定性方面均优于基础模型和广义线性模型，可实现对红松不同树干高度木材密度的准确估计。该模型为该区域人工红松木材质量分段评估、生物量和碳储量的精准估算以及经营管理提供了可靠的工具。

Abstract

[Objective] Plantation-grown Pinus koraiensis is an important timber and ecological tree species in the forest regions of Northeast China. The longitudinal variation in its stem wood density is crucial for wood quality sorting, and for estimating biomass and carbon stocks. However, it is difficult for traditional models to accurately capture its longitudinal variation characteristics. This study aims to analyze the longitudinal variation pattern of Pinus koraiensis wood density and develop a high-accuracy predictive model to provide a basis for the precise assessment of wood properties and biomass. [Method] Based on 402 wood density samples collected from 30 Pinus koraiensis trees in Mengjiagang forest farm, this study first selected the optimal basic model from nine candidate wood density models. On this basis, traditional and easily accessible stand variables (number of trees per hectare, basal area per hectare, average stand height, and average stand diameter at breast height) were introduced to construct a generalized linear model, and the continuous autoregressive error structure CAR(1) was adopted to reduce the autocorrelation of model residuals. Meanwhile, a wood density model was constructed based on the theory of generalized additive models (GAM), and the fitting effects of the six smoothing functions of GAM were compared. Finally, the predictive performance of different modeling approaches was compared using ten-fold cross-validation method. [Result] (1) The wood density of Pinus koraiensis exhibits a distinct nonlinear pattern along the stem longitudinal gradient, showing an overall trend of initially decreasing and then increasing with relative height. (2) Among the base models, our self-developed Model 9 achieved the best fitting performance. The generalized linear model developed based on Model 9 by introducing trees per hectare further improved the model fitting performance. Compared with Model 9, the adjusted coefficient of determination (R ²_adj) increased by 2.4%, MAE decreased by 0.7%. (3) The application of a continuous autoregressive error structure of order 1, CAR (1), effectively reduced residual autocorrelation in both the basic and generalized linear models. After correction, while the mean absolute error (MAE) values of the two models decreased by 2.4% and 2.5%, respectively, compared with those before correction. (4) The GAM constructed using cubic regression splines (CR) with variables including DBH, mean annual increment of DBH, crown width, relative height, and number of trees per hectare exhibited the best predictive capability. The ten-fold cross-validation results further confirmed that the GAM has superior robustness and generalization ability. Compared with the generalized linear model, its R ²_adj increased by 13.25% and the MAE decreased by 9.54%. [Conclusion] This study systematically constructed a longitudinal wood density model for the stems of Pinus koraiensis, and revealed its longitudinal variation pattern of "first decreasing and then increasing". The GAM is superior to the basic model and the generalized linear model in fitting performance, prediction accuracy, and stability, and can accurately estimate the wood density at any stem height of Pinus koraiensis. This model provides a reliable tool for segmented wood quality assessment, precise biomass and carbon stock estimation, and sustainable management of plantation-grown Pinus koraiensis in the region.

关键词

红松 / 木材密度 / 广义加性模型（GAM） / 纵向变异 / 连续自回归误差结构（CAR（1））

Key words

Pinus koraiensis / wood density / generalized additive models (GAM) / longitudinal variation / continuous autoregressive error structure of order 1 (CAR(1))

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基金资助

国家自然科学基金项目(32271866)