基于分段回归的人工红松冠形预估模型

Crown-shape model of a Pinus koraiensis plantation in northeastern China

利用黑龙江省孟家岗林场79株人工红松解析木4 538个枝条的实测数据,基于样条函数的分段回归技术,通过推导满足冠形曲线生物学约束（即梢头处树冠半径为0,拐点处树冠半径最大）连续分段函数,构建了人工红松的冠形曲线模型（分段抛物线方程、分段单分子式方程和分段幂函数方程）。采用模型的拟合优度指标、模型的检验指标及对模型拐点参数估计的合理性对备选模型进行评价,选出拟合人工红松冠形曲线的最优模型。采用模型再参数化方法,分别分析模型各参数与林木变量之间的相关性,最终在最优冠形曲线模型中加入胸径作为自变量,建立了人工红松树冠形状预估模型。研究结果表明：分段抛物线函数为描述人工红松冠形曲线的最优模型。人工红松冠形曲线参数及树冠大小与林木胸径（DBH）成正相关,经过再参数化后的树冠形状预估模型的调整决定系数（R2a）为0.659 6,估计标准误差（Sy.x）为0.524 5,模型的残差均方（MSE）为0.227 9,预估精度（p）为97.58%。随着DBH增大,红松冠形曲线拐点（相对冠深）出现的范围为0.72~0.95,平均值为0.81。总体上来看,以胸径为自变量、以稍头约束为条件的树冠形状预估模型能够很好的预测人工红松的树冠形状,为进一步估测红松树冠结构提供了基础。

Using the data of 4 538 branches from 79 Pinus koraiensis in Mengjiagang forest farm of Heilongjiang Province,northeastern China,we deduced continuous segmented function with biological constraints of tree crown profile（ crown width at top of tree is 0 and the maximum value at inflection point） based on the segmented regression of spline function theory,and developed the crown profile models（ i. e.segmented parabola equation,segmented Mitscherlich equation and segmented power equation） for Pinus koraiensis. The goodness-of-fitting index,validation results of the models and the reasonability from estimating the inflection points were used to evaluate all models and select the optimal model for predicting crown profile of Pinus koraiensis. With the re-parameterization of the model parameters and the analysis of the correlation between the parameters and tree variables,diameter at the breast height（ DBH） was introduced into the optimal model,and the crown-shape predicting model for Pinus koraiensis was established. The results showed that the segmented parabola function was the optimal equation to describe crown profile for Pinus koraiensis. The crown size and parameters of the crown profile were positively correlated with DBH. For the crown-shape predicting model after re-parameterization,the coefficient of determination（ R2a） was 0. 659 6,the standard error（ Sy. x） of estimation was 0. 524 5 and the mean square error（ MSE） was 0. 227 9. Meanwhile,the prediction precision（ p） was 97. 58%.With the increase of DBH,the range of inflection point of Pinus koraiensis crown profile（ relative crown depth） is between 0. 72- 0. 95 with a mean value of 0. 81. On the whole,the crow-shape predictingmodel with DBH as independent variable and the tree top as constraint performed well in predicting the crown profile for Pinus koraiensis,which provides basis for estimating crown structure of Pinus koraiensis in plantations.