基于混合效应模型的新疆天山云杉单木胸径预测模型构建

Predicting model construction of single tree DBH of Picea schrenkiana in Xinjiang of northwestern China based on mixed effects model

【目的】建立新疆天山云杉单木胸径生长模型,以期对天山云杉胸径生长进行预测,为天山云杉经营管理提供理论依据。【方法】以天山云杉为研究对象,基于新疆自治区一类清查数据中70块天山纯林复测样地,样地中测得活立木共计1914株,随机选取1531组数据作为训练数据,383组数据作为检验数据。对比分析传统单木胸径模型和混合效应模型在云杉单木胸径模型的应用,在运用R语言的nlme模块构建混合效应模型时考虑密度水平效应、样地效应以及嵌套两水平效应,并用平均绝对误差(E)、均方根误差(RMSE)、平均预估误差(MPE)、总相对误差(TRE)、调整决定系数(R^2adj)来检验模型的拟合效果。【结果】混合效应模型(R^2adj=0.762)优于传统胸径模型(R^2adj=0.505)。混合效应模型中,基于嵌套两水平混合效应模型最好,其平均绝对误差(∣E∣)、均方根误差(RMSE)、平均预估误差(MPE)、总相对误差(TRE)、调整决定系数(R^2adj)值分别为0.589 cm、0.804 cm、0.966%、-0.042%、0.899。混合效应模型拟合效果由高到低依次为:嵌套两水平混合效应模型(R^2adj=0.899)>样地混合效应模型(R^2adj=0.766)>密度水平混合效应模型(R^2adj=0.762)。幂函数能有效消除异方差结构的影响,一阶自回归矩阵AR(1)可以有效消除数据的时间相关效应。【结论】研究求得的天山云杉单木胸径生长混合效应模型可作为新疆天山云杉单木胸径预测的主要模型,其中嵌套密度水平效应和样地效应的混合效应模型对单木胸径的预测效果最好(R^2adj=0.899),此研究表明混合效应模型是新疆天山云杉单木胸径预测的有效方法,为大面积新疆天山云杉单木胸径预测提供理论基础及新的方法。

[Objective]This paper aims to establish a single tree DBH growth model of Picea schrenkiana in Xinjiang of northwestern China in order to predict the DBH growth of Picea schrenkiana and provide a theoretical basis for the forestry department to manage P.schrenkiana forest.[Method]Taking Picea schrenkiana as the research object,based on the 70 pieces of Tianshan Mountain pure forest retesting sample plots in Xinjiang,a total of 1914 viable standing trees were measured in the sample plots,and 1531 sets of data were randomly selected for training data,383 sets of data for test data.Contrasting and analyzing the application of traditional single-tree DBH model and mixed effects model in the spruce single-tree DBH model,considering the density level effect,sample plot effect and nesting two-level effect when using the R language nlme module to construct the mixed effects model,and using the average absolute error(E),root mean square error(RMSE),average prediction error(MPE),total relative error(TRE)to test the fitting effects of the model.[Result]The mixed effects model(R^2adj=0.762)was superior to the traditional breast diameter model(R^2adj=0.505).In the mixed effects model,that based on the nesting two-level was the best.The average absolute error(∣E∣),the root mean square error(RMSE),the average prediction error(MPE),the total relative error(TRE),and the adjustment decision coefficient(Ra2 dj)were 0.589 cm,0.804 cm,0.966%,-0.042%,0.899,respectively.The fitting effect of mixed effects model from high to low was:nesting two-level mixed effects model(R^2adj=0.899)>sample plot mixed effects model(R^2adj=0.766)>density level mixed effects model(R^2adj=0.762).The power function can effectively eliminate the influence of heteroscedastic structure.The first-order autoregressive matrix AR(1)can effectively eliminate the time-dependent effect of the data.[Conclusion]The mixed model of DBH growth of Picea schrenkiana can be used as the main model for the prediction of DBH diameter in the Picea schrenkiana of Xinjiang,in which the mixed effects model of nesting density level effect and sample plot effect is the best for predicting the DBH diameter(R^2adj=0.899).This study shows that the mixed effects model is an effective method for predicting the single tree DBH of the Picea schrenkiana in Xinjiang,and provides a theoretical basis and a new method for predicting the single tree DBH of the large-scale Xinjiang Picea schrenkiana.