基于空间自相关的天然蒙古栎阔叶混交林林木胸径-树高模型

Individual Diameter-Height Models for Mixed Quercus mongolica Broadleaved Natural Stands Based on Spatial Autocorrelation

【目的】考虑林木间的空间自相关,构建基于空间自相关的林木胸径-树高模型,为可持续经营天然混交林提供理论依据。【方法】以天然蒙古栎阔叶混交林为研究对象,选择适宜的线性化林木胸径-树高模型为基础模型(BM),应用3个同步自回归(SAR)模型即空间滞后模型(SLM)、空间误差模型(SEM)和空间Durbin模型(SDM)研究该混交林的林木胸径-树高模型。同时,将Delaunay三角网(DT)矩阵、逆距离一次幂(ID1)、逆距离二次幂(ID2)、逆距离五次幂(ID5)、球状变异函数(SV)矩阵、高斯变异函数(GV)矩阵和指数变异函数(EV)矩阵共7个空间加权矩阵应用于SAR模型中。利用普通最小二乘法(OLS)估计BM参数,极大似然法估计3个SAR模型参数,并对4个模型的回归参数进行T检验,对3个SAR模型的自回归参数进行似然比检验。选择Moran’s I(MI)指数比较分析BM、SLM、SDM和SEM 4个模型的残差空间自相关,选择决定系数(R2)、均方根误差(RMSE)和Akaike信息准则(AIC)3个拟合指标比较分析4个模型的拟合效果。【结果】空间加权矩阵SV的BM残差MI值大于1,因此以下结果分析中将不再考虑SV。其他6个空间加权矩阵的BM和SLM残差MI值均显著大于期望值I0,但SLM残差MI值较相同空间加权矩阵的BM残差MI值小。除了GV和ID1外,其他4个空间加权矩阵的SDM残差MI值均与I0差异不显著。除了ID1外,其他5个空间加权矩阵的SEM残差MI值均与I0差异不显著。3个SAR模型的3个拟合指标均优于BM。在相同的空间加权矩阵中,SDM和SEM的3个拟合指标非常接近,但均优于SLM。在SDM和SEM中,不同空间加权矩阵(除GV外)根据3个拟合指标从优至劣的排序为ID2>DT>ID>ID5>EV。无论采用哪个空间加权矩阵,3个SAR模型的回归参数β1均与BM中的β1相似,且均显著不为零。相比β1,SEM和BM中的β0相似,但SDM和SLM中的β0与BM中的β0不相似,并且随着空间加权矩阵的变化而变化。应用于SAR模型的所有空间加权矩阵中,利用ID1得出的自回归参数ρ、γ和λ均明显高于利用其他空间加权矩阵计算的值。GV只有在SEM中才能使自回归参数λ显著。除了GV外,利用其他5个空间加权矩阵得出的ρ、γ和λ均显著。【结论】应用于SAR模型的7个空间加权矩阵中,SV和ID1为不合理的空间加权矩阵。SLM只能降低模型残差的空间自相关,改善模型拟合效果较SDM和SEM差。只要选择合适的空间加权矩阵,SDM和SEM就可以消除模型残差的空间自相关,提高模型拟合效果,其中ID2是最好的空间加权矩阵。利用ID2和SEM构建以树种为哑变量的胸径-树高模型,从而得出基于空间自相关的蒙古栎、杨桦(山杨和白桦)、红松的胸径-树高模型。

【Objective】Considering spatial autocorrelation among individuals,individual diameter-height models based on spatial autocorrelation were constructed. It may provide a theoretical basis for sustainable management of natural mixed forests. 【Method】Three simultaneous autoregressive（ SAR） models,including spatial lag model（ SLM）,spatial errormodel（ SEM） and spatial Durbin model（ or called spatial mixed model）（ SDM） within seven spatial weight matrices,including Delaunay triangulation（ DT）,inverse distance raised to one power（ ID1）,inverse distance raised to two powers（ ID2）,inverse distance raised to five powers（ ID5）,spherical variogram（ SV）,gaussian variogram（ GV） and exponential variogram（ EV）,was used to construct individual diameter at breast height and height models of mixed Quercus mongolica broadleaved natural stands in Northeast China,and treating linearization base model（ BM） as a benchmark model. Model parameters of BM were estimated by ordinary least squares（ OLS）,model parameters of three SAR models were estimated by maximum likelihood. Model coefficients β0and β1of four models were tested by T-test,the autoregressive parameters ρ,γ and λ were all tested by likelihood ratio test. Moran＇s I（ MI） was selected to compared autocorrelation of four model residuals. Three statistics,i. e. coefficient of determination（ R2）,root mean square error（ RMSE） and Akaike information criterion（ AIC）,were regarded as the appropriate criteria to identify the model fitting among BM,SLM,SDM and SEM. 【Result】MI values of BM residuals were larger than 1,when applying SV into BM.Therefore,SV was the unreasonable spatial weight matrix and did not regard as a spatial weight matrix in the following result analysis. MI values of BM and SLM residuals were significantly larger than the expected value I0 of MI in the all spatial weight matrices（ except SV）. MI values of SLM residuals were smaller than those of BM using the same spatial weight matrix. The difference between MI values of SDM residuals and I0 was not significant in other four spatial weight matrices,except GV and ID1. Similarly,the difference between MI values of SEM residuals and I0 was not significant in other five spatial weight matrices,except ID1. Three criteria of three SAR models were all better than those of BM. Using the same spatial weight matrix,MI values of SDM were very similar to those of SEM,meanwhile,MI values of SDM and SEM were both larger than those of SLM. Different spatial weight matrices（ except GV） in SDM and SEM were sorted from best to worst according three criteria and the ranking was： ID2 DT ID ID5 EV. Model coefficients β1of three SAR were very similar to those of BM,regardless of which spatial weight matrix was used. Compared with β1,model coefficients β0of SEM were similar to those of BM,while model coefficients β0of SDM and SLM were different to those of BM,and were changed along with the different spatial weight matrix. Among all spatial weight matrices within three SAR models,the autoregressive parameters ρ,γ and λ using ID1 were larger higher than any other spatial weight matrix. GV only applied to SEM,rather than SDM,could make the autoregressive parameter λ significant not equal to zero. The autoregressive parameters ρ,γ and λ were all not equal to zero using five spatial weight matrices（ except GV）.【Conclusion】Among all spatial weight matrices applied in three SAR models,SV and ID1 are the unreasonable spatial weight matrices. SLM do not remove,but reduce the spatial autocorrelation of model residuals,and slightly improve the model fitting. Model fitting of SLM was worse than those of SDM and SEM. Selecting appropriate spatial weight matrices,SDM and SEM can remove the spatial dependence of model residuals and improve the model fitting. ID2 is the best one among these selected appropriate spatial weight matrices. The diameter-height models of Quercus mongolica,PopulusBetula（ Populus davidiana and Betula platyphylla） and Pinus koraiensis were constructed by species dummy variables SAR models based on ID2 and SEM.