干形是反映树干外部形态的重要指标,也是评价干材价值的重要依据,而削度方程是描述树木干形好坏的一个重要定量指标,其对干形模拟的准确性直接决定着树干材积和森林蓄积的估算结果。以河北省塞罕坝机械林场华北落叶松人工林为研究对象,基于4个常见的简单削度方程,模拟了260株样木的干形曲线,采用调整后决定系数(R_a²)、均方根误差(RMSE)、平均误差(ME)和平均误差绝对值(MAE)评价模型的拟合效果和检验效果,筛选最优的基础模型,并利用分位数回归技术,构建人工华北落叶松干形曲线模型。结果表明,4个简单削度方程中,Kozak方程对华北落叶松干形的拟合效果最好(R_a²=0.934, RMSE=1.985cm),检验结果也是最优的(ME=0.125cm, MAE=1.212cm)。因此,基于Kozak方程,结合分位数回归技术建立了华北落叶松干形曲线,相较于基础模型,分位数回归模型的拟合优度进一步提高。当分位点设置为0.1时,模型对靠近下部和上部的树干干形拟合效果较好;当分位点设置为0.5时,模型对位于中部的树干干形拟合效果较好;当分位点设置为0.9时,模型对树干基部的拟合效果较好。可见,分位数回归技术使模型具有更强的灵活性。

Stem shape is an important index to reflect the external shape of stem and it is also an important basis for evaluating the value of trunk.The taper equation is an important quantitative index to describe the quality of tree stem shape.The accuracy of its simulation of stem shape directly determines the estimation of trunk volume and forest volume.In this study,four simple taper equations were used to estimate the stem shape of planted Larixprincipis-rupprechtii and the model fit and validation were assessed byadjusted determination coefficient(R_a²),root mean square error(RMSE),mean error(ME)and absolute mean error(MAE).The optimal model was selected and the taper shape of Larixprincipis-rupprechtii was modelled by using quantile regression technology.Result showed that Kozak equation has the best fitting result(R_a²=0.934, RMSE=1.985cm)and the validation result(ME=0.125cm, MAE=1.212cm)on the stem shape among the four simple taper equations.Thus,the taper shape of Larixprincipis-rupprechtii was established by using quantile regression technology based on Kozak equation.Compared with the basic model,the goodness-of-fit of quantile regression model was improved.When the quantile is set to 0.1,the model has a better fitting effect on the stem shape near the lower and upper part of trunk,when the quantile is set to 0.5,the model has a better fitting effect on the trunk at the middle part of trunk,and when the quantile is set to 0.9,the model has a better fitting effect on the base of trunk.It can be seen that quantile regression technology makes the model more flexible.