不同林分起源的相容性生物量模型构建

目前为止已有不同方法构建生物量相容性模型,但不同林分起源的生物量相容性模型很少报道。针对此问题,以150株南方马尾松(Pinus masson iana)地上生物量数据为例,利用比例平差法和非线性联立方程组法建立不同起源地上生物量以及干材、干皮、树枝和树叶各分项生物量相容的通用性模型。根据分配层次不同,两种方法又各自考虑总量直接控制和分级联合控制两种方案。从直径、树高、地径、枝下高和冠幅5个林分变量中选取不同的变量构建一元、二元和三元生物量模型,并利用加权最小二乘回归法消除生物量模型中存在的异方差性。结果为:比例平差法和非线性联立方程组法都能有效保证各分项生物量总和等于总生物量,模型预测精度满足要求。总体而言,非线性联立方程组方法比比例平差方法精度高,同时两种方法中总量直接控制法比分级联合控制法预测效果好;各分项生物量模型本身作为权函数能有效消除异方差;各分项对应的三元生物量模型预测精度最高,其次是二元生物量模型,最低是一元生物量模型,但这些差异不是很大。总之,为权衡考虑模型预测精度和调查成本,建议把直径和树高作为协变量利用总量直接控制非线性联立方程组法对不同起源生物量建模。

Development of compatible biomass models for trees from different stand origin

Biomass equations for individual-trees have appeared frequently in the ecological and forestry literature over the last 60 years as biomass estimation is a prerequisite for studies on forest productivity, nutrient cycling and for calculating carbon sequestration, storage and other structural and functional attributes of forest ecosystems. Over the same period of time, the methods of developing biomass equations for total tree and component biomass have evolved from single equation least squares to multivariate adjustment in proportion and simultaneous equations, both linear and nonlinear. The single equation approach relates total tree biomass and its components such as stem, wood, bark, branches, and foliage to predictor variables such as diameter at breast height, height and sometime also crown width using log transformed data through least squares regression. The equation for each component is estimated separately without taking into account (1) the inherent correlation among the biomass components measured on the same sample trees and (2) the logical constraint between the sum of predicted biomass for tree components and the prediction for the total tree. As a result, biomass equations developed through this approach fall short of statistical efficiency in parameter estimation and lack compatibility among the component equations (Parresol 1999). The lack of compatibility means inconsistency in logic in the sense that the predicted values from summing the biomass equations of tree components do not equal to the predicted value from the equation for the total tree biomass. Development of compatible individual-tree biomass models were well reported in the literature, while how to construct these biomass models for trees from different stand origin has not been investigated so far. In this paper, generalized models on total above-ground biomass and its four components (stem wood, stem bark, branch, and foliage) for trees from different stand origin were established using the methods of adjustment in proportion and nonlinear simultaneous equations. Totally 150 Masson pine (Pinus masson iana) trees were sampled for biomass investigation in southern China. For the two approaches mentioned above, i.e. adjustment in proportion and nonlinear simultaneous equations, controlling jointly from level to level by ratio functions and controlling directly under total biomass by proportion functions were employed. Covariate variables of one-, two- and three-variable biomass models were obtained from five stand variable candidates of diameter at breast height, tree total height, diameter at ground level, height to crown base and crown width. Weighted least square regression was used to remove the heteroscedasticity of biomass models. The results showed that both methods of adjustment in proportion and nonlinear simultaneous equations could efficiently ensure that the total biomass is equal to the summary of its components with high prediction accuracy. However, the prediction accuracy of nonlinear simultaneous equations was generally much higher than that of adjustment in proportion. The approach of controlling directly by proportion functions was slightly better than the one controlling jointly by ratio functions. The function of each component biomass itself as weighted function could remove heteroscedasticity effectively. The biomass models for each component with three variables (diameter at breast height, height and crown width) had the highest prediction accuracy, following by the two variables (diameter at breast height and height), and the single variable (diameter at breast height) model. The discrepancies among the models were very small, however. For balancing the model prediction accuracy and survey cost in constructing biomass model for trees from different stand origin, we suggest adapting the nonlinear simultaneous equations of controlling directly under total biomass with diameter at breast height and height as covariables.