基于混合效应的华北落叶松次生林单木冠长模型

Crown length model of individual trees in Larix principis-rupprechtii secondary forests based on mixed-effect

【目的】为准确预估单木冠长,在再参数化的基础上构建基于混合效应的单木冠长模型,为华北落叶松区域经营、生产、科研提供理论依据及模型参考。【方法】以山西省五台山和庞泉沟地区116块样地2745株华北落叶松次生林为例,建立单木冠长模型,从9个冠长-胸径候选模型中选取最优基础模型;除胸径外还考虑其他6个林木、林分因子对冠长的影响,通过逐步回归分析选择影响最为显著的因子构建冠长再参数化模型;最后引入样地随机效应,构建含混合效应的华北落叶松次生林单木冠长模型,选用3个常用异方差消除函数中最优者消除混合效应模型的异方差性。【结果】9个候选模型尤以Logistic形式的冠长-胸径模型拟合精度最优,效果最好(R^(2)=0.5699,RMSE=3.8127,MAE=3.0223);其他6个林木、林分因子中高径比(HDR)和公顷株数(N)对冠长的影响最为显著,将显著性因子高径比(HDR)和公顷株数(N)纳入最优基础模型构建再参数化模型,模型确定系数(R^(2))从0.5699提升到0.7005,提升了22.9%,均方根误差(RMSE)从3.8127降低至3.1816,下降了16.6%,平均绝对误差(MAE)从3.0223降低至2.4107,下降了20.2%;在再参数化方法的基础上构建混合效应的单木冠长模型,引入样地水平作为随机效应因子作用在固定参数a上,混合效应模型确定系数(R^(2))从0.7005提升至0.8136,提升了16.1%,均方根误差(RMSE)从3.1816降低至2.5120,下降了21.0%,平均绝对误差(MAE)从2.4107降低至1.8373,下降了23.8%;选用指数方差函数能够有效地消除模型异方差性,残差分布范围更小,分布更均匀。【结论】在再参数化基础上构建混合效应模型能更加准确地预估林木冠长,为华北落叶松次生林区域性的森林经营活动提供科学依据。

【Objective】In this work,to accurately estimate the crown length of individual trees,the individual tree crown length model based on mixed-effect was constructed based on Re-parameterization,to provide a theoretical basis and model reference for the regional management,production and scientific research of Larix principis-rupprechtii.【Method】Taking 2745 Larix principisrupprechtii secondary forest trees in the 116 sample plots in Wutai Mountain and the Pangquangou area of Shanxi Province as the samples,the individual tree crown length model was established,and the optimal basic model was selected from 9 crown length-DBH candidate models.In addition to DBH,the effects of the other six forest and stand factors on crown length were applied,and the most significant factors were selected through stepwise regression analysis to construct a Re-parameterized model of crown length.Finally,the random effect of the sample plot was introduced to construct the individual tree crown length model of Larix principis-rupprechtii secondary forests with mixed-effect.The best of the three common heteroscedasticity elimination functions was selected to eliminate the heteroscedasticity of the mixed-effect model.【Result】Among the nine candidate models,the Logistic model of crown length-DBH model(R^(2)=0.5699,RMSE=3.8127,MAE=3.0223)had the best fitting accuracy.Among the other six factors,the height-to-diameter ratio(HDR)and the number of plants per hectare(N)had the most significant impacts on crown length.The significant factors height-to-diameter ratio(HDR)and the number of plants per hectare(N)were incorporated into the optimal basic model to build a Re-parametric model.The model determination coefficient(R^(2))changed from 0.5699 to 0.7005,increasing by 22.9%,and the root mean square error(RMSE)decreased from 3.8127 to 3.1816,reducing by 16.6%,and the mean absolute error(MAE)decreased from 3.0223 to 2.4107,reducing by 20.2%.Based on the parametric method,the mixed-effect model was constructed,and the sample level was introduced as a random effect factor to act on the fixed-parameter a.The determination coefficient(R^(2))of the mixed-effect model increased from 0.7005 to 0.8136,by 16.1%,and the root mean square error(RMSE)decreased from 3.1816 to 2.5120,by 21.0%,and the mean absolute error(MAE)decreased from 2.4107 to 1.8373,by 23.8%.The selection of exponential variance function can effectively eliminate the heteroscedasticity of the model,and the residual distribution range would be smaller and more uniform.【Conclusion】The results showed that the mixed-effect model based on Re-parameterization can accurately predict the forest crown length,which provides a scientific basis for the regional forest management activities of Larix principis-rupprechtii secondary forests.