塞罕坝华北落叶松人工林树冠外部轮廓模型

Crown Prediction Model of Larix principis-rupprechtii Plantation in Saihanba of Hebei Province,Northern China

【目的】构建树冠最大外部轮廓非线性混合效应模型和非线性分位数回归模型,为准确预测树冠生长发育规律及预估生产力提供科学依据。【方法】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58株解析木数据和1789个枝条解析数据,利用幂函数、修正Kozak方程、修正Weibull方程选取基础模型,构建华北落叶松人工林树冠外部轮廓非线性混合效应模型和非线性分位数回归模型。【结果】在幂函数、修正Kozak方程和修正Weibull方程中,幂函数拟合树冠外部轮廓效果较好,作为树冠外部轮廓基础模型;林分年龄(Age)、冠长(CL)、胸径(DBH)、树高(HT)、冠高比(CHR)、高径比(HDR)对树冠外部轮廓影响较大。在混合效应模型中,两水平混合效应模型优于单水平混合效应模型,可明显提高模型拟合精度,HDR相关的参数a 6考虑样地效应,相对着枝深度(RDINC)、CHR相关的参数a 4、a 5考虑样木效应,模型确定系数(R 2)为0.873,均方根误差(RMSE)为0.319 m,平均相对误差(MRE)为6.642 m。在分位数回归模型中,当分位数q=0.90时模型曲线最接近树冠最大外部轮廓,R 2为0.672。【结论】混合效应模型拟合精度较高,可准确描述树冠最大枝条的平均趋势。分位数回归模型可确定树冠最外部轮廓,在预测条件均值之外的研究中发挥重要作用。

【Objective】The crown of a tree is an important organ for material exchange and energy conversion.The nonlinear mixed effect model and the nonlinear quantile regression model of the maximum crown outline were constructed to provide a scientific basis for accurately predicting the growth and development law of the crown and its productivity.【Method】Taking Larix principis-rupprechtii plantation of Saihanba forest farm in Hebei Province as the research object,based on 1789 branches data of 58 trees,the power equation,modified Kozak and modified Weibull equation were selected as the basic models to construct a mixed effect model and a nonlinear quantile regression model for predicting the crown shape of L.principis-rupprechtii plantation.【Result】Among the power function,modified Kozak equation and modified Weibull equation,the power function equation had the best fitting effect of tree crown profile.The power function equation was chosen as the basic model of tree crown profile.Stand age(Age),diameter at breast height(DBH),height of the tree(HT),crown height ratio(CHR),and height to diameter ratio(HDR)had significant effects on fitting crown contour.In the mixed effect model,the two-level mixed effect model considering both plot and tree effects was superior to the single-level mixed effect model.The random effect of the plot was added to the HDR parameter,and the random effect of the sample was added to the RDINC(relative depth into crown)and CHR parameters.The model determination coefficient(R 2)was 0.873,the root mean square error(RMSE)was 0.319 m,and the mean relative error(MRE)was 6.642 m.In the quantile regression model,when q=0.90,the model curve model was the closest to the crown maximum profile,R 2 was 0.672.【Conclusion】The mixed-effect model might be a better fitting accuracy and could accurately describe the average trend of the largest branches of the canopy.The quantile regression model could determine the outermost contour of the canopy and may play an important role in research beyond the prediction of conditioned mean.