大兴安岭不同区域兴安落叶松可变指数削度方程

Variable-Exponent Taper Models for Dahurian Larch in Different Regions of Daxing'anling

【目的】基于林业上广泛应用的Kozak(1988),Kozak(1994),Kozak(2001)和Kozak(2002)可变指数削度方程,构建适合大兴安岭不同区域兴安落叶松树干削度方程,同时检验不同区域的显著性。【方法】采用大兴安岭3个区域的兴安落叶松样木干形数据,利用SAS软件的非线性回归SUR法拟合4个削度方程,采用调整确定系数(R2adj)、平均误差(MAB)、均方根误差(RMSE)、相对误差(MPB)、预估精度(P%)和多重共线性指标(CN)以及相应的残差分布图等对削度方程进行综合比较分析。区域性检验采用非线性额外平方和方法,该方法需要拟合完整模型和简化模型。【结果】1)Kozak(1988)和Kozak(1994)削度方程拟合和预估精度较高,但是存在较高的多重共线性问题;其他削度方程降低了模型的多重共线性,但可提高对树干上部的预测能力。2)不同区域模型的F检验分析发现,区域3与区域1和区域2的树干削度相差较大,区域1和区域2的树干削度相差较小,任何2个区域的对比检验都是显著的(P<0.000 1),说明模型在不同区域不能共用一套参数,应有不同的区域参数估计。3)从不同区域各模型的干曲线模拟可以看出,同一模型在3个区域的干曲线模拟结果不同,尤其模型(3)在3个区域中的干曲线更明显地体现出3个区域的不同。模型(1)、模型(2)和模型(4)在3个区域的干曲线模拟体现在区域1和区域2的模拟结果比较接近,区域3则与其有明显不同,该结果与F检验结果一致。不同区域对树木干曲线有显著影响,削度方程参数估计值在不同区域的错误应用会导致较大误差。【结论】Kozak(2002)可变指数削度方程在拟合统计量、残差分布图和多重共线性等方面都表现出了一致性,预估精度达99%以上,可作为大兴安岭3个区域兴安落叶松的最优削度方程。

【Objective】The aim of this study was to develop taper functions of dahurian larch（ Larix gmelinii） based on widely used variable-exponent taper models developed by Kozak（1988）,Kozak（1994）,Kozak（2001） and Kozak（2002）,and the significances of different regions were also tested. 【Method】Stem taper data of dahurian larch was collected from three regions of Daxing ＇anling. SUR method in SAS software was used to fit the four taper equations. Coefficient determination（ R^2_（adj））,mean absolute bias（ MAB）,root mean square error（ RMSE）,mean percentage of bias（ MPB） and prediction accuracy（ P%） were employed to evaluate the precision of different models combining multicollinearity（ CN）and graph of the residuals. The non-linear extra sum of squares method was used for regional comparison. The method required the fitting of full model and reduced model. 【Result 】1） Variable-exponent taper models developed by Kozak（1988） and Kozak（1994） were better based on goodness of fit statistics and prediction precision,but they had high multicollinearity. The other models decreased multicollinearity and improved prediction precision of upper stem diameters.2） F-test of regional comparison showed that stem taper in region 3 had large differences with region 1 and region 2. Stem taper in region 1 had small difference with region 2. Any two regional test showed significant difference（ P 0. 000 1）. It was indicated that any two regions could not use the same parameter estimates and separated parameter estimates werenecessary. 3） Through the stem taper curve simulations in three regions,it could be seen that the same model showed the different taper curve simulations in three regions,especially the taper curves of model 3 showed significant difference in three regions. The taper curve simulations of other models showed small differences with region 1 and region 2,and significant difference was found for region 3. The results of simulations were consistent with the results from F-test.Different region had a significant effect on tree stem curve. Incorrectly application of taper models in different regions would result in larger prediction error. 【Conclusion 】 Taper model developed by Kozak（ 2002） showed the consistent performance on fitting statistics,residual distribution,and multicollinearity. The prediction precision was more than99%,and could be selected as the best taper equation for the three regions of Daxing＇anling.