基于贝叶斯法的针阔混交林树高与胸径混合效应模型

Height-Diameter Relationship for Conifer Mixed Forest Based on Bayesian Nonlinear Mixed-Effects Model

【目的】在多树种多层次针阔混交林中,基于贝叶斯混合效应模型法构建树高与胸径关系的混合效应模型,以提高预测模型参数稳定性,为揭示混交林多树种生长规律、资源分配差异及森林质量精准提升提供科学依据。【方法】以河北省塞罕坝机械林场华北落叶松和白桦针阔混交林为研究对象,基于112块标准地(30 m×30 m)调查数据,选取6个包含不同林分因子的理论方程作为构建混交林不同树种树高与胸径关系的基础模型,选择出拟合精度较高的模型,分别采用两水平非线性混合效应模型法和贝叶斯混合效应模型法构建立包含哑变量的多树种树高与胸径关系模型。【结果】包含林分优势高和林分断面积组合变量的Richards方程拟合效果最好,模型确定系数(R^2)、均方根误差(RMSE)和绝对误差(Bias)分别为0.8495、2.3786和0.3654;贝叶斯混合效应模型法拟合精度略高于传统非线性混合效应模型法:基于传统非线性混合效应模型法的华北落叶松树高与胸径关系模型的RMSE和Bias分别为0.9304和0.1034,白桦树高与胸径关系模型的RMSE和Bias分别为0.9827和0.1126;基于贝叶斯混合效应模型法的华北落叶松树高与胸径关系模型的RMSE和Bias分别为0.9105和0.0968,白桦树高与胸径关系模型的RMSE和Bias分别为0.9633和0.1002。【结论】基于贝叶斯混合效应模型法构建的非线性混合效应模型,充分考虑混交林多树种树高与胸径关系模型参数的不确定性,模型预测效果更具可靠性和稳定性。

【Objective】 This paper established the nonlinear mixed effects model for height-diameter relationship based on Bayesian statistics in multi-storied and multi-species mixed forests. The purpose of this study was to provide some references for growth regularity of multiple tree species, differences in resource allocation and precision improvement of forest quality.【Method】 A total of 112 temporary plots were established in Larix principis-rupprechtii and Betula platyphylla mixed forest of Saihanba national forest park, Hebei Province, China. Plot size was 30 m×30 m. We selected 6 typical models including different stand factors to fit height-diameter relationship. And the best-fit model was chose as the basis for building mixed-effects models by the method of Bayesian and nonlinear mixed models. We also added dummy variables to the mixed-effects models in order to solve intra-plot variability resulting from species difference. The goodness-of-fit criteria used were the coefficient of determination(R^2), the absolute error of estimate(Bias)and the root mean square error(RMSE).【Result】 Richards equation including dominant height and basal area of stand provided the most accurate prediction of height with the highest R2(0.849 5), the lowest Bias(2.378 6)and RMSE(0.365 4).The fitting accuracy of Bayesian non-linear mixed effect method was slightly higher than that of traditional non-linear mixed effects model method. Parameter estimation method of traditional non-linear mixed effect model had the best fits with the fit statistics values(RMSE=0.930 4;Bias=0.103 4)for L. principis-rupprechtii and values(RMSE=0.982 7;Bias=0.112 6)for B. platyphylla. Parameter estimation method of Bayesian nonlinear mixed effect model had the best fits with the fit statistics values(RMSE=0.910 5;Bias=0.096 8)for L. principis-rupprechtii and values(RMSE=0.963 3;Bias=0.100 2)for B. platyphylla.【Conclusion】 The non-linear mixed effect model based on Bayesian theory considered the uncertainties of parameters in the model of tree height-diameter relationship of multi-species. The prediction results have better reliability and stability.