【目的】为了准确预估长白落叶松-水曲柳4种不同行间混交方式(行间混交比例分别为1∶1、2∶2、3∶3、5∶5)的单木冠长,采用联立方程组模型分别构建了长白落叶松和水曲柳的冠长模型。【方法】基于黑龙江省尚志国有林场管理局的长白落叶松-水曲柳混交林54块标准地的样木数据,从3种非线性的基础冠长模型中选取最优冠长模型,以单分子式模型为树高曲线的基础模型,并将混交比例(Z_i)和树木在混交带内位置(K)作为哑变量,加入其他树木变量、林分变量和竞争因子,分别构建长白落叶松和水曲柳的冠长模型;基于最优冠长模型和树高曲线模型建立联立方程组模型,采用非线性似乎不相关回归(NSUR)的方法进行参数估计,并对所构建的模型进行评价。【结果】长白落叶松冠长与高径比呈负相关,与林木树高和林分优势高之比呈正相关;水曲柳冠长与高径比呈负相关,与林木胸径和林分优势木胸径之比呈正相关;长白落叶松树高与长白落叶松优势木平均高呈正相关,水曲柳树高与水曲柳优势木平均高呈正相关。联立方程组预估长白落叶松冠长和树高的调整后决定系数 ( R_{\mathrm{a}}^2 )分别为0.478 1和0.821 6,联立方程组预估水曲柳冠长和树高的 R_{\mathrm{a}}^2 分别为0.395 8和0.752 9。【结论】构建冠长和树高联立方程组模型不仅具有较好的拟合效果及预测精度,还解决了冠长与树高之间内在相关性的问题。因此,本研究所构建的冠长模型可以很好地预测东北地区混交林内长白落叶松和水曲柳的冠长,为进一步研究混交林树木树冠结构提供依据。

【Objective】 To accurately predict the crown length of Larix olgensis and Fraxinus mandshurica trees mixed by rows with four different mixing methods (1∶1, 2∶2, 3∶3, 5∶5), crown length models for L. olgensis and F. mandshurica were developed using simultaneous equation models. 【Method】 The data for sample trees of L. olgensis and F. mandshurica in mixed stands were collected from 54 permanent sample plots in the Shangzhi Administrative Bureau of National Forestry Centers in Heilongjiang Province. The best crown length model was selected from three nonlinear basic models, and the Mitscherlich model was selected as the basic model of the height-diameter model. The mixed proportion (Z_i) and the tree position (K) in mixed rows were taken as dummy variables. Other tree variables, as well as stand variables and competition factors were also added. Based on the optimal crown length and height-diameter model, the simultaneous equations model of the crown length and height were developed, respectively. The nonlinear seemingly uncorrelated regression (NSUR) method was used to estimate the parameters, and the fitting effects of the models was evaluated. 【Result】The ratio of the total tree height to DBH was negatively correlated with the crown length of L. olgensis, and the ratio of tree height to dominant tree height was positively correlated with the crown length of L. olgensis. The height-diameter ratio was negatively correlated with the crown length of F. mandshurica and the ratio of tree diameter at breast height to dominant tree diameter was positively correlated with the crown length of F. mandshurica. The average stand height of L. olgensis was positively correlated with the height of L. olgensis, while the dominant tree height of F. mandshurica was positively correlated with the height of F. mandshurica. For the simultaneous equations, the adjusted coefficients of determination ( R_{\mathrm{a}}^2 ) of the crown length and height of L. olgensis were 0.478 1 and 0.821 6, respectively. For the simultaneous equations, the R_{\mathrm{a}}^2 of the crown length and height of F. mandshurica were 0.395 8 and 0.752 9, respectively. 【Conclusion】 Constructing a simultaneous equation system for the crown length and tree height not only has good fitting effects and prediction accuracy, but also solves the problem of the inherent correlation between the crown length and height. Therefore, the crown length models established in this study can accurately predict the crown length of L. olgensis and F. mandshurica in the rows of mixed plantations, thereby providing a basis for a further study on the crown structure in mixed plantations.