Nonlinear mixed-effects height-diameter model of Pinus koraiensis
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摘要: 以吉林省汪清林业局的蒙古栎阔叶混交林和云冷杉阔叶混交林24块固定样地中的2598株红松为研究对象,利用Chapman-Richards方程建立了不含随机效应与含随机效应的单木树高-胸径简单模型和广义模型。模型拟合和检验的评价指标主要包括调整决定系数(R2a)、平均相对误差绝对值(RMA)和均方根误差(RMSE)。对于混合效应模型,设计了随机抽取、抽胸径最大的树、抽胸径最小的树和抽平均木4种抽样方案计算随机参数,通过对比4种抽样设计下模型的误差统计量,分析了不同抽样设计下样本数量和预测精度的关系。结果表明:基于混合效应模型的红松单木树高-胸径模型拟合效果(简单模型的R2a在0.753~0.886之间,RMA在11.3%~15.1%之间,RMSE在1.38~2.01m之间;广义模型的R2a在0.754~0.886之间,RMA在11.1%~15.0%之间,RMSE在1.38~2.01m之间)优于不含随机参数的红松单木树高-胸径模型(简单模型的R2a在0.502~0.868之间,RMA在12.2%~17.8%之间,RMSE在1.42~2.65m之间;广义模型的R2a在0.711~0.877之间,RMA在11.6%~17.2%之间,RMSE在1.41~2.10m之间);包含随机效应的简单模型和广义模型拟合效果没有明显的差异,表明基于混合效应模型的单木树高-胸径简单模型可以很好地描述树高-胸径关系在不同森林类型、不同样地间的差异,因此不需要在树高-胸径模型中增加其他自变量;抽取平均木的抽样设计优于其他3种抽样设计,且抽取4株平均木时,预测精度提升最为明显,综合预测精度和调查成本的考虑,在实践中应用包含随机效应的红松树高-胸径模型时,推荐在样地中抽取4株平均木测量其树高来估计随机参数。Abstract: The Chapman-Richards function was used to construct individual height-diameter model for Pinus koraiensis. The data were collected from mixed deciduous stands of Mongolian oak-deciduous (Quercus mongolica) stands and mixed stands of spruce-fir and deciduous trees in Wangqing Forestry Bureau, Jilin Province of northeastern China. A total of 2 598 trees in 24 permanent plots were used for model development. Simple and generalized height-diameter model with and without random effect parameters were tested. Model evaluation criteria included adjusted determination coefficient (R2a), relative mean absolute error (RMA) and root mean square error (RMSE). For mixed-effects models, different sample sizes of four sampling designs, i.e., random sampling, the largest diameter tree sampling, the smallest diameter tree sampling and intermediate diameter tree sampling for random parameter estimation were compared and the relationship between sample size and predicted accuracy was analyzed. The results showed that the goodness-of-fit of individual height-diameter models based on mixed-effects model (R2a of simple models ranged between 0.753-0.886, RMA between 11.3%-15.1%, RMSE between 1.38-2.01m; R2a of generalized models ranged between 0.754-0.886, RMA between 11.1%-15.0%, RMSE between 1.38-2.01m) was better than that of individual height-diameter model without random effect parameters (R2a of simple models ranged between 0.502-0.868, RMA between 12.2%-17.8%, RMSE between 1.42-2.65m; R2a of generalized models ranged from 0.711-0.877, RMA between 11.6%-17.2%, RMSE between 1.41-2.10m). Furthermore, the difference of goodness-of-fit between simple and generalized height-diameter models with mixed-effects was not significant, which may lead us to a conclusion that individual height-diameter simple model with mixed-effects can describe the variation of height-diameter relationship in different forest types and plots, thus additional variables were not be necessary in height-diameter model. In addition, intermediate diameter tree sampling was better than others and predicted accuracy can be improved obviously when four mean diameter trees were sampled per plot. Taking predicted accuracy and investigation cost into account, we recommend sampling of four intermediate diameter trees per plot for practical application of the mixed-effects height-diameter model of Pinus koraiensis.
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