基于混合模型的油松林分蓄积量预测模型的建立

Establishment of predicting models for Pinus tabulaeformis stands volume based on mixed models

【目的】建立预估精度高的林分蓄积量混合模型,为北京地区不同初期密度油松林分提供个性化模型方程,为森林经营和采伐利用提供重要理论依据。【方法】以北京地区76块油松连续清查样地为研究对象,按初期的油松林分密度(ID)将油松样地分为Ⅰ(ID<400株/hm^2)、Ⅱ(400≤ID<800株/hm^2)、Ⅲ(800≤ID<1 200株/hm^2)、Ⅳ(1 200≤ID<1 600株/hm^2)、Ⅴ(ID≥1 600株/hm^2)5个水平,选用以断面积和优势木平均高为自变量的线性模型构建油松蓄积量基础模型,在基础模型上分别考虑油松林分的密度水平效应、样地效应和嵌套两水平效应,用R语言的nlme模块建立油松混合效应模型,并用平均绝对误差||、均方根误差RMSE、决定系数R^2 3个评价指标检验模型的拟合效果。【结果】拟合嵌套两水平混合模型决定系数R^2为0.998 2,高于密度水平效应和样地效应2个单水平混合模型,且||和RMSE均小于2个单水平混合模型;嵌套两水平混合模型的、RMSE分别为0.069 8和0.100 6,比基础模型降低了78.86%和82.39%。指数函数异方差结构和[ARMA(1,1)]时间序列相关性结构加入混合模型后,模型拟合精度均有一定提高。【结论】单水平和嵌套两水平混合模型拟合精度均高于基础模型,嵌套两水平混合效应模型拟合精度优于基础模型和单水平混合模型,指数函数能够消除数据间的异方差,[ARMA(1,1)]结构能够较好地表达样地间的误差相关性。

【Objective】This study established high precision stand volume models to provide personalized model equations for different density stands in Beijing,which would provide theoretical basis for forest management and harvesting.【Method】Using the periodically inventory data of 76 Pinus tabulaeformis plots in Beijing,P.tabulaeformis stands were divided into five levels by different initial densities（ID）including Ⅰ（ID400 strain/hm^2）,Ⅱ（400≤ID800 strain/hm^2）,Ⅲ（800≤ID1 200 strain/hm^2,Ⅳ（1 200≤ID100 strain/hm^2）,and Ⅴ（ID≥1 600 strain/hm^2）.Choosing basal area and average height of dominant trees as independent variables,the basic linear model of P.tabulaeformis volume was constructed.Based on the basic model,P.tabulaeformis mixed effects models were constructed considering densitylevel effect and plot effect and using R language NLME.Then absolute mean error（｜｜）,root mean square errors（RMSE）,and coefficient of determination（R^2）were used to evaluate the models.【Result】The R^2 of two-level mixed model was 0.998 2,higher than that of single-level mixed models of density level effect and plot effect,while both｜｜and RMSEof the two-level mixed model were smaller than the two singlelevel mixed models.The｜｜and RMSEof the two-level mixed model were 0.069 8 and 0.100 6,which were 78.86% and 82.39% lower than the basic model,respectively.When heteroscedasticity of exponential function and[ARMA（1,1）]time series correlation structure were added to the mixed model,the fitting precision was improved.【Conclusion】The precision of both single level mixed models and two-level mixed model were better than that of basic model.The two-level mixed model was better than basic model and single level mixed models.Exponential function variance structures could effectively remove the heteroscedasticity in the data,and[ARMA（1,1）]structure can express the error correlation between plots.