林业科学  2019, Vol. 55 Issue (2): 75-86 PDF
DOI: 10.11707/j.1001-7488.20190208
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#### 文章信息

Zeng Weisheng, He Dongbei, Pu Ying, Xiao Qianhui.

Individual Tree Biomass and Volume Equation System with Region and Origin in Variables for Pinus massoniana in China

Scientia Silvae Sinicae, 2019, 55(2): 75-86.
DOI: 10.11707/j.1001-7488.20190208

### 作者相关文章

1. 国家林业和草原局调查规划设计院 北京 100714;
2. 国家林业和草原局中南林业调查规划设计院 长沙 410014

Individual Tree Biomass and Volume Equation System with Region and Origin in Variables for Pinus massoniana in China
Zeng Weisheng1, He Dongbei2, Pu Ying1, Xiao Qianhui2
1. Academy of Forest Inventory and Planning, National Forestry and Grassland Administration Beijing 100714;
2. Central South Forest Inventory and Planning Institute, National Forestry and Grassland Administration Changsha 410014
Abstract: 【Objective】Climate change has increased the need of information on amount of forest biomass. The purpose of this study is to develop compatible individual tree biomass and volume equations, providing a quantitative basis on accurate estimation of forest biomass. 【Method】Based on the mensuration data of above-and belowground biomass from 301 and 104 destructive sample trees of Masson pine (Pinus massoniana) in southern China, respectively, one-and two-variable systems, which combined aboveground biomass and stem volume equations with belowground biomass equation, and ensured them compatible with biomass conversion factor and root-to-shoot ratio equations, were developed using dummy variable modeling approach and error-in-variable simultaneous equations approach, and effects of region and origin on estimation of biomass and volume were analyzed.【Result】The coefficients of determination (R2) of one-and two-variable compatible individual tree biomass and volume equations for Masson pine developed in this study were more than 0.92, whereas the mean prediction errors (MPEs) of above-and belowground biomass equations were less than 4% and 8%, respectively. For estimation of aboveground biomass and stem volume of Masson pine, two-variable equations were significantly better than one-variable equations, for the F-statistics between one-and two-variable aboveground biomass and stem volume equations were greatly larger than the critical F value. But for estimation of belowground biomass, one-variable were even better than two-variable ones. Effects of region and origin on estimation of both one-and two-variable aboveground biomass equations were not significant, indicating that aboveground biomass equations of Masson pine were generalized on national level. Furthermore, the general allometric biomass model M=0.3ρD7/3presented by Zeng et al.(2012) was proved to be applicable in practice. For estimation of belowground biomass of Masson pine, models in different regions were significantly different. For trees with the same diameter, estimate of belowground biomass in the region of modeling population 1(south-eastern part of Yangtze River basin) was larger than that in the region of modeling population 2(central-western part of Yangtze River basin).For estimation of stem volume of Masson pine, two-variable model was not affected by region and origin, whereas one-variable model was affected by origin. For trees with the same diameter, estimate of stem volume in a planted stand was larger than that in a natural stand. 【Conclusion】Integrating dummy variable into error-in-variable simultaneous equations is a practical approach, which not only can ensure the compatibility among several target variables, but also can develop simultaneously a system even though numbers of above-and belowground biomass observations are very different. The biomass equations, volume equations, and compatible biomass conversion factor equations and root-to-shoot ratio equations developed for Masson pine in this study meet the need of precision requirements to relevant regulation, and can be used in application.
Key words: aboveground biomass    belowground biomass    dummy variable    error-in-variable    simultaneous equations

1 数据与方法 1.1 数据采集

1.2 模型建立

 $y = {\beta _0}{x_1}^{{\beta _1}}{x_2}^{{\beta _2}} \cdots {x_j}^{{\beta _j}} + \varepsilon 。$ (1)

 ${M_{\rm{a}}} = {a_0}{D^{{a_1}}}{H^{{a_2}}} + \varepsilon ;$ (2)
 ${M_{\rm{b}}} = {b_0}{D^{{b_1}}}{H^{{b_2}}} + \varepsilon ;$ (3)
 $V = {c_0}{D^{{c_1}}}{H^{{c_2}}} + \varepsilon 。$ (4)

1.2.1 相容性联立方程组

 $\left\{ \begin{array}{l} {M_{\rm{a}}} = {a_0}{D^{{a_1}}}{H^{{a_2}}} + \varepsilon ;\\ {M_{\rm{b}}} = {b_0}{D^{{b_1}}}{H^{{b_2}}}I + \varepsilon ;\\ V = {c_0}{D^{{c_1}}}{H^{{c_2}}} + \varepsilon ;\\ {\rm{BCF}} = {a_0}{D^{{a_1}}}{H^{{a_2}}}/{c_0}{D^{{c_1}}}{H^{{c_2}}} + \varepsilon ;\\ {\rm{RSR}} = {b_0}{D^{{b_1}}}{H^{{b_2}}}I/{a_0}{D^{{a_1}}}{H^{{a_2}}} + \varepsilon 。\end{array} \right.$ (5)

1.2.2 含地域和起源因子的联立方程系统

 $\left\{ \begin{array}{l} {M_{\rm{a}}} = \left({{a_0} + {a_{01}}J + {a_{02}}K} \right){D^{\left({{a_1} + {a_{11}}J + {a_{12}}K} \right)}} + \varepsilon ;\\ {M_{\rm{b}}} = \left({{b_0} + {b_{01}}J + {b_{02}}K} \right){D^{\left({{b_1} + {b_{11}}J + {b_{12}}K} \right)}} \cdot I + \varepsilon ;\\ V = \left({{c_0} + {c_{01}}J + {c_{02}}K} \right){D^{\left({{c_1} + {c_{11}}J + {c_{12}}K} \right)}} + \varepsilon ;\\ {\rm{BCF}} = \left({{a_0} + {a_{01}}J + {a_{02}}K} \right){D^{\left({{a_1} + {a_{11}}J + {a_{12}}K} \right)}}/\\ \;\;\;\;\left[ {\left({{c_0} + {c_{01}}J + {c_{02}}K} \right){D^{\left({{c_1} + {c_{11}}J + {c_{12}}K} \right)}}} \right] + \varepsilon ;\\ {\rm{RSR}} = \left({{b_0} + {b_{01}}J + {b_{02}}K} \right){D^{\left({{b_1} + {b_{11}}J + {b_{12}}K} \right)}} \cdot I/\\ \;\;\;\;\left[ {\left({{a_0} + {a_{01}}J + {a_{02}}K} \right){D^{\left({{a_1} + {a_{11}}J + {a_{12}}K} \right)}}} \right] + \varepsilon 。\end{array} \right.$ (6)

1.3 模型评价

 ${R^2} = 1 - \sum {{{\left({{y_i} - {{\hat y}_i}} \right)}^2}} /\sum {{{\left({{y_i} - \bar y} \right)}^2}} ;$ (7)
 ${\rm{SEE}} = \sqrt {\sum {{{\left({{y_i} - {{\hat y}_i}} \right)}^2}} /\left({n - p} \right)} ;$ (8)
 ${\rm{TRE}} = \sum {\left({{y_i} - {{\hat y}_i}} \right)} /\sum {{{\hat y}_i}} \times 100;$ (9)
 ${\rm{MPE}} = {t_\alpha } \cdot \left({{\rm{SEE}}/\bar y} \right)/\sqrt n \times 100。$ (10)

 $F = \frac{{\left({{\rm{SS}}{{\rm{E}}_2} - {\rm{SS}}{{\rm{E}}_1}} \right)/\left({{\rm{d}}{{\rm{f}}_2} - {\rm{d}}{{\rm{f}}_1}} \right)}}{{{\rm{SS}}{{\rm{E}}_1}/{\rm{d}}{{\rm{f}}_1}}}。$ (11)

 $F = \frac{{\frac{1}{2}\left({a\sum {{y_i}} + b\sum {{x_i}{y_i}} - 2\sum {{x_i}{y_i}} + \sum {x_i^2} } \right)}}{{\frac{1}{{n - 2}}\left({\sum {{{\hat y}_i}} - a\sum {{y_i}} - b\sum {{x_i}{y_i}} } \right)}}。$ (12)

2 结果与分析

 ${\rm{TRE}} \le {\rm{MPE}} \cdot {{t'}_a}/{t_a} \cdot \sqrt {n/n'} 。$ (13)

3 讨论

 图 1 不同建模总体的地下生物量实测值与估计值之间的对比 Fig. 1 Comparison between observed and estimated values of belowground biomass in different modeling populations
4 结论