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    李想, 董利虎, 李凤日. 基于联立方程组的人工樟子松枝下高模型构建[J]. 北京林业大学学报, 2018, 40(6): 9-18. DOI: 10.13332/j.1000-1522.20170428
    引用本文: 李想, 董利虎, 李凤日. 基于联立方程组的人工樟子松枝下高模型构建[J]. 北京林业大学学报, 2018, 40(6): 9-18. DOI: 10.13332/j.1000-1522.20170428
    Li Xiang, Dong Lihu, Li Fengri. Building height to crown base models for Mongolian pine plantation based on simultaneous equations in Heilongjiang Province of northeastern China[J]. Journal of Beijing Forestry University, 2018, 40(6): 9-18. DOI: 10.13332/j.1000-1522.20170428
    Citation: Li Xiang, Dong Lihu, Li Fengri. Building height to crown base models for Mongolian pine plantation based on simultaneous equations in Heilongjiang Province of northeastern China[J]. Journal of Beijing Forestry University, 2018, 40(6): 9-18. DOI: 10.13332/j.1000-1522.20170428

    基于联立方程组的人工樟子松枝下高模型构建

    Building height to crown base models for Mongolian pine plantation based on simultaneous equations in Heilongjiang Province of northeastern China

    • 摘要:
      目的基于黑龙江省帽儿山实验林场、横头山林场、孟家岗林场的61块樟子松人工林固定样地的5211株样木调查数据,构建了树高模型与枝下高模型的联立方程组。
      方法首先,从8种常用的标准树高曲线,选出拟合效果较好的2个模型作为树高曲线的备选模型。再以5个枝下高预估模型作为基础模型,通过引入林木及林分变量(林木大小,竞争因子,立地条件)采用最优子集回归法筛选出3个变量少且拟合效果较好的模型作为枝下高备选模型。将树高曲线备选模型与枝下高备选模型分别两两联立,建立树高与枝下高联立方程组模型,采用似乎不相关回归(SUR)对模型参数进行求解。最后,对联立方程组进行评价。
      结果树高(H)和枝下高(HCB)与林分断面积(G)和优势木平均高(H0)呈正相关。最优的联立方程组预估树高时调整后相关系数(Ra2)为0.9520,均方根误差(RMSE)为1.17m;预估枝下高时的Ra2为0.9066,RMSE为1.36m,并且模型的各项检验指标数值较小。
      结论整体来看,联立方程组的拟合效果较好,预估精度较高,同时联立方程组解决了树高与枝下高的内在相关性问题。本文所建立的含林分因子的树高模型与枝下高模型联立方程组可以很好地预估不同林分条件下樟子松人工林的树高和枝下高,为进一步研究樟子松树冠结构和动态提供了基础。

       

      Abstract:
      ObjectiveBased on the data of 5211 sample trees in 61 permanent sample plots in Mongolian pine plantations from Maoershan Experimental Forest Farm, Hengtoushan Forest Farm, Mengjiagang Forest Farm in Heilongjiang Province of northeastern China, the simultaneous equations for tree height model and height to crown base model were developed.
      MethodAt first, 2 alternative height-diameter models had been selected by comparing the goodness of fit for 8 height-diameter models. From 5 basic height to crown base(HCB)models, 3 best HCB models including tree and stand variables (tree size, competition index, site condition) were selected as alternative models using the method of all subset regression. Based on the seeming unrelated regression (SUR), the parameters of the simultaneous equations model of height and HCB were estimated considering each kind of combinations for 2 alternative height-diameter models and 3 alternative HCB models, respectively. Finally, we evaluated the fitting effect of the simultaneous equation model.
      ResultThe results showed that H and HCB were positively correlated with basal area (G) and average height of dominant tree (H0). For the best simultaneous equations, the coefficient determination (Ra2) was 0.9520 and the root-mean-square error (RMSE) was 1.17m by fitting height (H), the Ra2 was 0.9066, and RMSE was 1.36m by fitting HCB. The validation values of the best simultaneous equations were smaller.
      ConclusionOn the whole, the simultaneous equations developed performed well in predicting the tree H and HCB simultaneously with the least predicting errors, and the model could handle correlations between tree H and HCB. The simultaneous equations considering stand variables developed in this paper could be suitable for predicting H and HCB for Mongolian pine plantations with different stand conditions and it will provide basis for future research on the crown structure and dynamics.

       

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