【目的】基于非线性分位数回归方法构建大兴安岭落叶松(Larix gmelinii)树干削度方程,并分析比较基本模型与不同分位数(τ=0.1、0.2、0.3、0.4、0.5、0.6、0.7、0.8、0.9)模型,利用树干不同高度的上部直径进行矫正分位数组合模型预测精度,为落叶松天然林干形的精准预测提供理论依据。【方法】以大兴安岭壮志林场212株落叶松树干干形数据为研究对象,基于非线性分位数回归方法和Max and Burkhart分段削度方程,利用SAS软件中NLP过程拟合各分位数分段削度方程,把树干相对高20%、30%、40%、50%、60%、70%处的直径以及胸径到树尖的中间位置(50%^*)的树干上部直径引入到分段削度方程中进行矫正,并以平均误差(MAB)和相对误差(MPB)为评价指标对削度方程进行对比分析。【结果】Max-Burkhart分段削度方程在9个不同的分位点都可以得到参数估计值,因此分位数回归削度模型可以评价在不同分位数的预测能力。未矫正的分位数(τ=0.5、0.6)模型的预测精度略优于基本模型。准确地选择矫正位置至关重要,与未矫正的基本模型相比,利用树干相对高20%和70%处的直径进行矫正不能提高各分位数组合模型的预测精度,利用树干相对高30%、40%、50%、60%处的直径以及胸径到树尖中间位置的树干上部直径进行矫正的大多数分位数组合(3、5、7、9个分位数组合)模型的预测精度都能得到提高,总体使用矫正位置分位数组合模型的预测精度顺序为40%>50%^*>50%> 60%>30%>20%>70%。最佳的矫正位置为树干相对高40%处,并以3个分位数的组合(τ=0.3、0.5、0.7)模型预测精度最高,与未矫正的基本模型相比,MAB和MPB均下降13.5%。【结论】在削度方程中引入一个合理的矫正位置可以提高模型的预测精度,其中,最佳矫正位置为树干相对高40%处,最优模型为3个分位数组合(τ=0.3、0.5、0.7)模型。在实际应用中,如果不考虑矫正时,建议采用分位数τ=0.5削度方程的参数估计值。

【Objective】 The aim of this study was to develop a stem taper equation based on the quantile regression method for Larix gmelinii in Greater Khingan Mountains. We compared and analyzed the prediction precision of basic models, different quantile (τ=0.1, 0.2, 0.3, 0.4, 0.5, 0.6, 0.7, 0.8, 0.9) models, and quantile group models using different upper-stem diameters. These studies provide a theoretical basis for the precise prediction of the natural forest taper of L. gmelinii. 【Method】 The stem taper data of 212 L. gmelinii in Greater Khingan Mountains, Songling Forest Bureau, were the research object. Based on the nonlinear quantile regression method and Max and Burkhart segmented taper equation, the nonlinear programming (NLP) method in SAS software was used to fit the stem taper equation of different quantiles. Calibration of the taper equations was carried out using the upper-stem diameter measured at the relative heights of 20%, 30%, 40%, 50%, 60%, 70%, and the midpoint between the breast height and the tip of the tree (50%^*). The mean absolute bias (MAB) and mean percentage of bias (MPB) were used as statistical criteria to compare the calibrated stem taper equations. 【Result】 The parameters of the Max and Burkhart segmented taper equations based on nine different quantiles were obtained, allowing the prediction ability of the quantile regression taper model in different quantiles to be evaluated. The prediction accuracy of the uncalibrated quantile models at the quantile (τ=0.5, 0.6) was slightly better than the uncalibrated basic model. Accurate choices of the localized position were essential. Compared with the uncalibrated basic model, the prediction accuracy of each quantile group model for the calibrated stem taper using the upper-stem diameter measured at relative heights of 20% and 70% was not improved. The prediction accuracy of the most quantile group (3, 5, 7, 9) models calibrated using the upper stem measurements at relative heights of 30%, 40%, 50%, 60% and the midpoint between the breast height and the tip of the tree was improved. The overall prediction accuracy using a quantile group model for the calibrated positions was 40%>50%^*>50%>60%>30%>20%>70%. The best calibration position was the relative height of 40% of the tree, and the three quantile (τ=0.3, 0.5, 0.7) group model had the highest prediction accuracy. Both MAB and MPB decreased by 13.5% compared to the uncalibrated basic model. 【Conclusion】 Introducing a reasonable calibration position in the taper equation improved the prediction accuracy of the models. The best calibration position was the relative height of 40% of the tree with the group of three quantiles (τ =0.3, 0.5, 0.7). In practical applications, if the calibration is not considered, it is recommended that the quantile (τ =0.5) should be used.