兴安落叶松树干削度和材积相容模型

Compatible stem taper and volume models for dahurian larch

描述了相容性非线性联立方程组模型在树干削度和材积建模方面的应用及联立方程组模型参数估计的方法。以黑龙江省带岭林业局人工落叶松为研究对象,以Max和Burkhart分段削度模型作为基础模型,构建了3个具有不同拐点的树干削度和材积系统。削度和材积系统拥有一套参数。为了使内生变量(endogenous variables)误差同时最小化,利用SAS软件模型模块中的似乎不相关回归过程(seemingly unrelated regression,SUR)解决联立方程组模型系统的参数估计。采用确定系数、绝对误差、相对绝对误差、均方根误差、相对均方根误差等模型评价指标对不同模型系统的精度进行比较分析。结果表明:具有2个拐点参数的Max和Burkhart分段削度和材积模型系统拟合精度是最高的。当考虑带皮直径时,拐点发生在树高下部0.09H处和上部0.77H处;当考虑去皮直径时,拐点发生在树高下部0.08H处和上部0.75H处。模型检验进一步证明该模型系统提供了最好的直径和材积预测精度。

The study describes the application of compatible nonlinear equation systems in developing stem taper and volume models and methods of parameter estimation.Three compatible stem taper and volume systems with different inflection points were developed for dahurian larch（Larix gmelinii Rupr.） plantations located in Dailing Forest Bureau,Heilongjiang Province of northeastern China based on a Max and Burkhart segmented taper model.Taper and volume systems share the same parameters.To concurrently minimize error in endogenous variables,seemingly unrelated regression（SUR） procedure of the PROC MODEL in SAS software was used to obtain parameter estimates of equation systems.Coefficient determination,absolute bias,relative absolute bias,root mean square error and relative root mean square error were employed to evaluate the precision of different model systems.The results showed that Max and Burkhart segmented taper and volume model systems with two inflection points provided best precision of model fitting.The lower and upper stem inflection points of dahurian larch were found to be 0.09H and 0.77H at tree height for diameter outside bark,and 0.08H and 0.75H for diameter inside bark.Model validation further confirms that this model system provides the best precision of diameter and volume prediction.