Mixed effect models for predicting breast height diameter from stump diameter of Oriental beech in Göldağ

Diameter at breast height (DBH) is the simplest, most common and most important tree dimension in forest inventory and is closely correlated with wood volume, height and biomass. In this study, a number of linear and nonlinear models predicting diameter at breast height from stump diameter were developed and evaluated for Oriental beech (Fagus orientalisLipsky) stands located in the forest region of Ayancık, in the northeast of Turkey. A set of 1,501 pairs of diameter at breast height-stump measurements, originating from 70 sample plots of even-aged Oriental beech stands, were used in this study. About 80 % of the otal data (1,160 trees in 55 sample plots) was used to fit a number of linear and nonlinear model parameters; the remaining 341 trees in 15 sample plots were randomly reserved for model validation and calibration response. The power model data set was found to produce the most satisfactory fits with the Adjusted Coefficient of Determination, R2adj (0.990), Root Mean Square Error, RMSE (1.25), Akaike’s Information Criterion, AIC (3820.5), Schwarz’s Bayesian Information Criterion, BIC (3837.2), and Absolute Bias (1.25). The nonlinear mixed-effect modeling approach for power model with R2adj(0.993), AIC (3598), BIC (3610.1), Absolute Bias (0.73) and RMSE (1.04) provided much better fitting and precise predictions for DBH from stump diameter than the conventional nonlinear fixed effect model structures for this model. The calibration response including tree DBH and stump diameter measurements of the four largest trees in a calibrated sample plot in calibration produced the highest Bias, -5.31 %, and RMSE, -6.30 %, the greatest reduction percentage.

胸径（Diameter at breast height, DBH）是森林资源调查中最为简便、常用且关键的林木维度指标，与木材蓄积量、树高及生物量均呈紧密相关。本研究针对土耳其东北部阿扬哲克（Ayancık）林区的东方山毛榉（Fagus orientalis Lipsky）林分，构建并评估了一系列基于伐根直径（stump diameter）预测胸径的线性与非线性模型。
本研究共采集了70块同龄东方山毛榉林分样地的1501组胸径-伐根直径测量数据对。其中约80%的总数据集（55块样地内的1160株林木）用于拟合多组线性与非线性模型的参数；剩余15块样地中的341株林木被随机预留，用于模型验证与校准响应分析。
研究表明，幂函数模型（power model）的拟合效果最优，其调整决定系数（Adjusted Coefficient of Determination, R²adj）为0.990、均方根误差（Root Mean Square Error, RMSE）为1.25、赤池信息准则（Akaike’s Information Criterion, AIC）为3820.5、施瓦茨贝叶斯信息准则（Schwarz’s Bayesian Information Criterion, BIC）为3837.2，绝对偏差（Absolute Bias）为1.25。
相较于该模型的传统非线性固定效应（nonlinear fixed effect）模型结构，针对幂函数模型采用非线性混合效应（nonlinear mixed-effect）建模方法，并引入校准样地内4株最大林木的胸径与伐根直径测量数据作为校准响应，可获得更优异的拟合效果与更精准的预测结果，其调整决定系数达0.993、AIC为3598、BIC为3610.1、绝对偏差为0.73，RMSE为1.04。
该校准方案对应的偏差为-5.31%，均方根误差为-6.30%，为所有校准策略中降幅最大的一项。