南京地区马尾松多元混合效应材积模型研建

摘要

In order to accurately fit the relationship among different diameters at breast height(DBH), heights and volumes of Pinus massoniana Lamb trees in Nanjing, the related mathematical standard models were established with Yamamoto standard volume model and multivariate nonlinear mixed effects model based on the data of 531 P.massoniana trees from 28 pieces 20 m×20 m square plots. The correlation indexes of the Yamamoto standard volume model was 0.964 92, the standard error of the estimate was 0.004 0, and the total relative deviation, the mean relative error, the mean estimate error, the absolute value of mean relative error were less than 3%. The correlation indexes of the multivariate nonlinear mixed effects model was 0.999 97, the standard error of the estimate was 0.000 049 85, and the total relative deviation, the mean relative error, the mean estimate error, the absolute value of mean relative error were less than 0.3%. The results show that the two models have good fitting results and high accuracy. The adaptability test shows that the total relative deviation, the mean relative error, the mean estimate error, the absolute value of mean relative error, absolute residual error and the standard deviation were less than 3%, and the F-value of statistics of the two models were far less than critical value, which shows that the two models have better adequacy and the multivariate nonlinear mixed effects volume model has better fitting results, higher accuracy and better adequacy than the Yamamoto standard volume model.%为了精确拟合南京地区马尾松林木胸径、树高与材积的相关关系，基于28块20 m×20 m 的方形样地的531株马尾松样木数据，分别采用山本式材积模型和多元非线性混合效应模型拟合了马尾松胸径、树高与材积的相关关系。结果显示：山本式材积模型的相关指数为0.96492，估计值的标准误为0.0040，总相对偏差、平均相对误差、平均预估误差和平均相对误差绝对值均小于3%，多元非线性混合效应模型的相关指数为0.99997，估计值的标准误为0.00004985，总相对偏差、平均相对误差、平均预估误差和平均相对误差绝对值均小于0.3%，表明两个材积模型有很高的拟合优度和精度，适应性检验结果显示，山本式二元材积模型和多元非线性混合效应材积模型的平均相对误差、总相对偏差、平均相对误差绝对值、绝对残差和标准偏差均小于3%，统计量 F 值小于临界值，表明两个材积模型的适应性较强；与山本式二元材积模型相比，多元非线性混合效应材积模型的拟合优度和精度更高，适应性更强。