大兴安岭不同区域落叶松相容性材积方程及异方差研究

目的]对不同区域立木相容性材积方程以及不同异方差校正方法进行详细对比分析,建立相容性材积方程预估大兴安岭不同区域落叶松的立木材积。方法]以大兴安岭3个不同区域的落叶松为研究对象,采用误差变量联立方程组的方法构建不同区域立木相容性材积方程。采用非线性额外平方和的方法(F检验)进行区域性检验。使用多种权函数分别对3个区域存在异方差的材积方程进行加权回归。结果]表明:任何2个区域的立木材积方程都有显著不同(P0.000 1),区域1和区域3的材积相差较大,区域2与区域1和区域3的材积相差较小。不同区域立木材积方程的错误应用会导致较大的预测误差。在参数稳定性和评价指标方面,加权估计会优于普通最小二乘估计。基于平均相对误差(MRE)和总相对误差(TRE),区域1(-0.11、0.97)、区域2(0.04、0.08)和区域3(1.04、0.93)的最优权函数分别为1/F(x)、1/D4.99、1/D3.38。结论]立木材积方程是森林调查和林分生长与收获模型的主要组成部分,本文所构建3个区域的相容联立方程组模型预测误差均不超过±3%。建立相容性立木材积方程时应考虑其异方差的影响。最优权函数没有统一的形式。为尽可能得到稳定的参数估计,在加权回归估计过程中应选用多种权函数进行对比分析。

Compatible Tree Volume Equations and Heteroscedasticity for Dahurian Larch in Different Region of Daxing'anling

Objective] Making a detailed comparative analysis of compatible volume models in different regions and different heteroscedasticity correction methods, developing compatible volume equations to estimate different regions for Dahurian larch (Larix gmelini Rupr.) in Daxing''anling.Method] Regional differences in volume models were examined and tested using the nonlinear extra sum of squares method (F-test). Weighted regression was used to decrease the heteroscedasticity of volume equations in three regions using variety forms of weight functions.Result] The results indicated that the volume models were significantly different among different regions (P<0.0001). The volume model in region 1 had the largest difference with region 3, the volume model in region 2 had smaller differences with region 1 and region 3.Incorrectly applying volume model in different regions would result in larger prediction error. Weighted estimation will be better than the ordinary least squares estimation in terms of parameters stability and evaluation index. Based on MRE and TRE, the best weighting functions are 1/F(x), 1/D^4.99, 1/D^3.38 for region 1(-0.11, 0.97), region 2(0.04, 0.08), and region 3(1.04, 0.93) respectively.Conclusion] Individual tree volume model is a major component of forest inventory and growth and yield model. Prediction errors of compatible volume models were within ±3% in three different regions. Compatible volume models should consider the phenomena of heteroscedasticity, and the optimal weight functions of individual tree volume models don''t have a uniform format. To get the stability of parameters estimation, different weight functions should be analyzed in the process of the weighted regression.