基于广义加性模型的樟子松树干削度方程研建

Research on stem taper equation of Scots pine based on generalized additive model

【目的】基于广义加性模型理论,构建樟子松的广义加性树干削度方程,并和林业上精度较高的变指数削度方程曾伟生等(1997)、Bi(2000)以及Kozak(2004)进行预测精度比较。【方法】以大兴安岭樟子松为研究对象,使用胸径、树高和不同部位高度及该部位树干直径及其变形构建广义加性削度方程,利用R软件mgcv软件包gamm函数对广义加性模型进行拟合,拟合过程中采用6种样条函数:B样条函数(BS)、三次回归样条函数(CR)、Duchon样条函数(DS)、高斯过程平滑样条函数(GP)、P样条函数(PS)和薄板回归样条函数(TP)。使用留一交叉检验法对模型进行检验。【结果】(1)将相对直径作为因变量,将胸径的平方、相对树高的算术平方根和树高作为自变量构建了最优的广义加性削度方程结构。(2)拟合结果表明,除CR外,其他光滑样条函数表现了相似的拟合结果,且均优于变指数削度方程的统计指标。(3)交叉检验结果表明,除CR光滑样条函数外,广义加性模型(BS,DS,GP,PS,TP)总体与拟合结果基本一致,即预测精度都优于曾伟生等(1997)、Bi(2000)和Kozak(2004)模型,其中广义加性模型中BS模型的预测精度最高,变指数削度方程中Kozak(2004)预测精度最高。(4)通过对比BS和Kozak(2004)模型的干曲线模拟发现,Kozak(2004)在预测小树树干上部时误差较大,而BS在模拟小树和大树上都具有较高的精度。【结论】广义加性模型是构建削度方程的一种非参数方法,基于BS样条函数的广义加性削度方程预测精度最高,适合大兴安岭地区樟子松的干形预测。

[Objective]Based on the theory of generalized additive model,stem taper equation was constructed for Scots pine(Pinus sylvestris).Accurate variable exponent taper equations such as Zeng et al.(1997),Bi(2000)and Kozak(2004)in forestry were used for comparison.[Method]The generalized additive taper equation was constructed using DBH,tree height,the height at different stem parts,the diameter at different tree heights and their transformation based on taper data of Scots pine.The model was fitted using the gamm function in mgcv library of the R software.Six smooth splines were chosen for fitting process,i.e.B-spline function(BS),cubic regression spline function(CR),Duchon spline function(DS),Gaussian process smooth spline function(GP),P-spline function(PS)and thin plate regression spline function(TP).The models were validated using leave-one-out cross-validation method.[Result](1)The optimal generalized additive model form of taper equation was constructed by response variable relative diameter and explanation variable square of DBH,total height and the square root of relative height.(2)The fitting results showed that the generalized additive taper equations were similar and better than parametric taper equation except for CR function.(3)The cross validation results showed that the generalized additive models(BS,DS,GP,PS and TP)were basically consistent with the fitting results except for CR,i.e.they were superior to parametric taper equation of Zeng et al.(1997),Bi(2000)and Kozak(2004).The BS model had the highest prediction accuracy in the generalized additive models.Kozak(2004)had the highest prediction accuracy in the variable exponential taper equations.(4)Through the simulation of stem curves of BS and Kozak(2004)models,it was found that Kozak(2004)had a large error in predicting the upper part of the stem of a small tree.However,BS had higher accuracy in simulating small tree and large tree.[Conclusion]The generalized additive model is a nonparametric method for constructing taper equation.The generalized additive taper equation based on BS spline has the highest prediction accuracy.It’s suitable for the prediction of the shape of Scots pine.