﻿ 广东主要乡土阔叶树种含年龄和胸径的单木生物量模型
 林业科学  2019, Vol. 55 Issue (2): 97-108 PDF
DOI: 10.11707/j.1001-7488.20190210
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#### 文章信息

Xue Chunquan, Xu Qihu, Lin Liping, He Xiao, Luo Yong, Zhao Han, Cao Lei, Lei Yuancai.

Biomass Models with Breast Height Diameter and Age for Main Nativetree Species in Guangdong Province

Scientia Silvae Sinicae, 2019, 55(2): 97-108.
DOI: 10.11707/j.1001-7488.20190210

### 作者相关文章

1. 广东省林业调查规划院 广州 510520;
2. 中国林业科学研究院资源信息研究所 北京 100091

Biomass Models with Breast Height Diameter and Age for Main Nativetree Species in Guangdong Province
Xue Chunquan1,2, Xu Qihu1, Lin Liping1, He Xiao2, Luo Yong1, Zhao Han2, Cao Lei2, Lei Yuancai2
1. Guangdong Institute of Forestry Inventory and Planning Guangzhou 510520;
2. Research Institute of Forest Resource Information Techniques, CAF Beijing 100091
Key words: tree age    biomass model    dummy variable    simultaneous system of equations    compatibility    origin

1 研究区概况、数据和方法 1.1 研究区概况

1.2 数据采集 1.2.1 单木生物量建模数据

1.2.2 解析木年龄测定

1.3 研究方法

1.3.1 以胸径和年龄为自变量的生物量模型

 $B = {\alpha _0}\cdot{D^{{\alpha _1}}}{T^{{\alpha _2}}} + \varepsilon ;$ (1)
 $B = {\alpha _0}\cdot{D^{{\alpha _1}}}{H^{{\alpha _2}}} + \varepsilon ;$ (2)
 $B = {\alpha _0} \cdot {({D^2}H)^{{\alpha _1}}} + \varepsilon 。$ (3)

1.3.2 考虑起源对生物量的影响

 $B = ({\alpha _0} + S \cdot {{\rm{b}}_0}) \cdot {D^{({\alpha _1} + S \cdot {{\rm{b}}_1})}} \cdot {T^{({\alpha _2} + S \cdot {{\rm{b}}_2})}} + \varepsilon ;$ (4)
 $B = ({\alpha _0} + S \cdot {{\rm{b}}_0}) \cdot {D^{({\alpha _1} + S \cdot {{\rm{b}}_1})}} \cdot {H^{({\alpha _2} + S \cdot {{\rm{b}}_2})}} + \varepsilon ;$ (5)
 $B = ({\alpha _0} + S \cdot {{\rm{b}}_0}) \cdot {({D^2}H)^{({\alpha _1} + S \cdot {{\rm{b}}_1})}} + \varepsilon 。$ (6)

1.3.3 含有哑变量的地上生物量各组分非线性联立方程组

 $\left\{ \begin{array}{l} {B_1} = \frac{1}{{1 + {g_1}\left(x \right) + {g_2}\left(x \right) + {g_3}\left(x \right)}} \times {g_0}\left(x \right);\\ {B_2} = \frac{{{g_1}\left(x \right)}}{{1 + {g_1}\left(x \right) + {g_2}\left(x \right) + {g_3}\left(x \right)}} \times {g_0}\left(x \right);\\ {B_3} = \frac{{{g_2}\left(x \right)}}{{1 + {g_1}\left(x \right) + {g_2}\left(x \right) + {g_3}\left(x \right)}} \times {g_0}\left(x \right);\\ {B_4} = \frac{{{g_3}\left(x \right)}}{{1 + {g_1}\left(x \right) + {g_2}\left(x \right) + {g_3}\left(x \right)}} \times {g_0}\left(x \right)。\end{array} \right.$ (7)

 $\left\{ \begin{array}{l} {B_1} = \\ \frac{1}{{1 + ({\alpha _1} + S \cdot {a_{s1}}) \cdot {D^{({b_1} + S \cdot {{\rm{b}}_{s1})}}} \cdot {T^{({c_1} + S \cdot {{\rm{c}}_{s1}})}} + ({\alpha _2} + S \cdot {a_{s2}}) \cdot {D^{({b_2} + S \cdot {{\rm{b}}_{s2})}}} \cdot {T^{({c_2} + S \cdot {{\rm{c}}_{s2}})}} + ({\alpha _3} + S \cdot {a_{s3}}) \cdot {D^{({b_3} + S \cdot {{\rm{b}}_{s3})}}} \cdot {T^{({c_3} + S \cdot {{\rm{c}}_{s3})}}}}}{g_0}\left({D, T} \right);\\ {B_2} = \\ \frac{{({\alpha _1} + S \cdot {a_{s1}}) \cdot {D^{({b_1} + S \cdot {{\rm{b}}_{s1})}}} \cdot {T^{({c_1} + S \cdot {{\rm{c}}_{s1}}})}}}{{1 + ({\alpha _1} + S \cdot {a_{s1}}) \cdot {D^{({b_1} + S \cdot {{\rm{b}}_{s1})}}} \cdot {T^{({c_1} + S \cdot {{\rm{c}}_{s1})}}} + ({\alpha _2} + S \cdot {a_{s2}}) \cdot {D^{({b_2} + S \cdot {{\rm{b}}_{s2})}}} \cdot {T^{({c_2} + S \cdot {{\rm{c}}_{s2})}}} + ({\alpha _3} + S \cdot {a_{s3}}) \cdot {D^{({b_3} + S \cdot {{\rm b}_{s3})}}} \cdot {T^{({c_3} + S \cdot {{\rm{c}}_{s3})}}}}}{g_0}\left({D, T} \right);\\ {B_3} = \\ \frac{{({\alpha _2} + S \cdot {a_{s2}}) \cdot {D^{({b_2} + S \cdot {{\rm{b}}_{s2})}}} \cdot {T^{({c_2} + S \cdot {{\rm{c}}_{s2}}})}}}{{1 + ({\alpha _1} + S \cdot {a_{s1}}) \cdot {D^{({b_1} + S \cdot {{\rm{b}}_{s1})}}} \cdot {T^{({c_1} + S \cdot {{\rm{c}}_{s1}})}} + ({\alpha _2} + S \cdot {a_{s2}}) \cdot {D^{({b_2} + S \cdot {{\rm{b}}_{s2})}}} \cdot {T^{({c_2} + S \cdot {{\rm{c}}_{s2}})}} + ({\alpha _3} + S \cdot {a_{s3}}) \cdot {D^{({b_3} + S \cdot {{\rm{b}}_{s3})}}} \cdot {T^{({c_3} + S \cdot {{\rm{c}}_{s3})}}}}}{g_0}\left({D, T} \right);\\ {B_4} = \\ \frac{{({\alpha _3} + S \cdot {a_{s3}}) \cdot {D^{({b_3} + S \cdot {{\rm{b}}_{s3})}}} \cdot {T^{({c_3} + S \cdot {{\rm{c}}_{s3})}}}}}{{1 + ({\alpha _1} + S \cdot {a_{s1}}) \cdot {D^{({b_1} + S \cdot {{\rm{b}}_{s1})}}} \cdot {T^{({c_1} + S \cdot {{\rm{c}}_{s1}})}} + ({\alpha _2} + S \cdot {a_{s2}}) \cdot {D^{({b_2} + S \cdot {{\rm{b}}_{s2})}}} \cdot {T^{({c_2} + S \cdot {{\rm{c}}_{s2}})}} + ({\alpha _3} + S \cdot {a_{s3}}) \cdot {D^{({b_3} + S \cdot {{\rm{b}}_{s3})}}} \cdot {T^{({c_3} + S \cdot {{\rm{c}}_{s3})}}}}}{g_0}\left({D, T} \right)。\end{array} \right.$ (8)
 $\left\{ \begin{array}{l} {B_1} = \\ \frac{1}{{1 + ({\alpha _1} + S\cdot{a_{s1}})\cdot{D^{({b_1} + S\cdot{{\rm{b}}_{s1})}}}\cdot{H^{({c_1} + S\cdot{{\rm{c}}_{s1}})}} + ({\alpha _2} + S\cdot{a_{s2}})\cdot{D^{({b_2} + S\cdot{{\rm{b}}_{s2})}}}\cdot{H^{({c_2} + S\cdot{{\rm{c}}_{s2}})}} + ({\alpha _3} + S\cdot{a_{s3}})\cdot{D^{({b_3} + S\cdot{{\rm{b}}_{s3})}}}\cdot{H^{({c_3} + S\cdot{{\rm{c}}_{s3})}}}}}{g_0}\left({D, H} \right);\\ {B_2} = \\ \frac{{({\alpha _1} + S\cdot{a_{s1}})\cdot{D^{({b_1} + S\cdot{{\rm{b}}_{s1})}}}\cdot{H^{({c_1} + S\cdot{{\rm{c}}_{s1})}}}}}{{1 + ({\alpha _1} + S\cdot{a_{s1}})\cdot{D^{({b_1} + S\cdot{{\rm{b}}_{s1})}}}\cdot{H^{({c_1} + S\cdot{{\rm{c}}_{s1}})}} + ({\alpha _2} + S\cdot{a_{s2}})\cdot{D^{({b_2} + S\cdot{{\rm{b}}_{s2})}}}\cdot{H^{({c_2} + S\cdot{{\rm{c}}_{s2}})}} + ({\alpha _3} + S\cdot{a_{s3}})\cdot{D^{({b_3} + S\cdot{{\rm{b}}_{s3})}}}\cdot{H^{({c_3} + S\cdot{{\rm{c}}_{s3})}}}}}{g_0}\left({D, H} \right);\\ {B_3} = \\ \frac{{({\alpha _2} + S\cdot{a_{s2}})\cdot{D^{({b_2} + S\cdot{{\rm{b}}_{s2})}}}\cdot{H^{({c_2} + S\cdot{{\rm{c}}_{s2})}}}}}{{1 + ({\alpha _1} + S\cdot{a_{s1}})\cdot{D^{({b_1} + S\cdot{{\rm{b}}_{s1})}}}\cdot{H^{({c_1} + S\cdot{{\rm{c}}_{s1}})}} + ({\alpha _2} + S\cdot{a_{s2}})\cdot{D^{({b_2} + S\cdot{{\rm{b}}_{s2})}}}\cdot{H^{({c_2} + S\cdot{{\rm{c}}_{s2}})}} + ({\alpha _3} + S\cdot{a_{s3}})\cdot{D^{({b_3} + S\cdot{{\rm{b}}_{s3})}}}\cdot{H^{({c_3} + S\cdot{{\rm{c}}_{s3})}}}}}{g_0}\left({D, H} \right);\\ {B_4} = \\ \frac{{({\alpha _3} + S\cdot{a_{s3}})\cdot{D^{({b_3} + S\cdot{{\rm{b}}_{s3})}}}\cdot{H^{({c_3} + S\cdot{{\rm{c}}_{s3})}}}}}{{1 + ({\alpha _1} + S\cdot{a_{s1}})\cdot{D^{({b_1} + S\cdot{{\rm{b}}_{s1})}}}\cdot{H^{({c_1} + S\cdot{{\rm{c}}_{s1}})}} + ({\alpha _2} + S\cdot{a_{s2}})\cdot{D^{({b_2} + S\cdot{{\rm{b}}_{s2})}}}\cdot{H^{({c_2} + S\cdot{{\rm{c}}_{s2}})}} + ({\alpha _3} + S\cdot{a_{s3}})\cdot{D^{({b_3} + S\cdot{{\rm{b}}_{s3})}}}\cdot{H^{({c_3} + S\cdot{{\rm{c}}_{s3})}}}}}{g_0}\left({D, H} \right)。\end{array} \right.$ (9)
 $\left\{ \begin{array}{l} {B_1} = \\ \frac{1}{{1 + ({\alpha _1} + S\cdot{a_{s1}})\cdot{D^2}{H^{({b_1} + S\cdot{b_{s1}})}} + ({\alpha _2} + S\cdot{a_{s2}})\cdot{D^2}{H^{({b_2} + S\cdot{{\rm{b}}_{s2}})}} + ({\alpha _3} + S\cdot{a_{s3}})\cdot{D^2}{H^{({b_3} + S\cdot{{\rm{b}}_{s3}})}}}}{g_0}({D^2}H);\\ {B_2} = \\ \frac{{({\alpha _1} + S\cdot{a_{s1}})\cdot{D^2}{H^{({b_1} + S\cdot{{\rm{b}}_{s1}})}}}}{{1 + ({\alpha _1} + S\cdot{a_{s1}})\cdot{D^2}{H^{({b_1} + S\cdot{{\rm{b}}_{s1}})}} + ({\alpha _2} + S\cdot{a_{s2}})\cdot{D^2}{H^{({b_2} + S\cdot{{\rm{b}}_{s2}})}} + ({\alpha _3} + S\cdot{a_{s3}})\cdot{D^2}{H^{({b_3} + S\cdot{{\rm{b}}_{s3}})}}}}{g_0}({D^2}H);\\ {B_3} = \\ \frac{{({\alpha _2} + S\cdot{a_{s2}})\cdot{D^2}{H^{({b_2} + S\cdot{{\rm{b}}_{s2}})}}}}{{1 + ({\alpha _1} + S\cdot{a_{s1}})\cdot{D^2}{H^{({b_1} + S\cdot{{\rm{b}}_{s1}})}} + ({\alpha _2} + S\cdot{a_{s2}})\cdot{D^2}{H^{({b_2} + S\cdot{{\rm{b}}_{s2}})}} + ({\alpha _3} + S\cdot{a_{s3}})\cdot{D^2}{H^{({b_3} + S\cdot{{\rm{b}}_{s3}})}}}}{g_0}({D^2}H);\\ {B_4} = \\ \frac{{({\alpha _3} + S\cdot{a_{s3}})\cdot{D^2}{H^{({b_3} + S\cdot{{\rm{b}}_{s3}})}}}}{{1 + ({\alpha _1} + S\cdot{a_{s1}})\cdot{D^2}{H^{({b_1} + S\cdot{{\rm{b}}_{s1}})}} + ({\alpha _2} + S\cdot{a_{s2}})\cdot{D^2}{H^{({b_2} + S\cdot{{\rm{b}}_{s2}})}} + ({\alpha _3} + S\cdot{a_{s3}})\cdot{D^2}{H^{({b_3} + S\cdot{{\rm{b}}_{s3}})}}}}{g_0}({D^2}H)。\end{array} \right.$ (10)

1.4 模型评价

 $R_{{\rm{adj}}}^2 = 1 - \left({1 - \frac{{\mathop \sum \limits_{i = 1}^n {{({{\hat y}_i} - {y_i})}^2}}}{{\mathop \sum \limits_{i = 1}^n {{({y_i} - \bar y)}^2}}}} \right) \cdot \frac{{n - 1}}{{n - p}};$ (11)
 ${\rm{SEE}} = \sqrt {\mathop \sum \limits_{i = 1}^n {{({{\hat y}_i} - {y_i})}^2}/\left({n - p} \right)} ;$ (12)
 ${\rm{MPE}} = {t_\alpha } \cdot \left({{\rm{SEE}}/\bar y} \right)/n \times 100;$ (13)
 ${\rm{TRE}} = \mathop \sum \limits_{i = 1}^n ({y_i} - {{\hat y}_i})/\mathop \sum \limits_{i = 1}^n {{\hat y}_i} \times 100。$ (14)

 $F = \frac{{{\rm{(SS}}{{\rm{E}}_{{\rm{base}}}}{\rm{ - SS}}{{\rm{E}}_{{\rm{dumb}}}}{\rm{)/(d}}{{\rm{f}}_{{\rm{base}}}}{\rm{ - d}}{{\rm{f}}_{{\rm{dumb}}}}{\rm{)}}}}{{{\rm{SS}}{{\rm{E}}_{{\rm{dumb}}}}{\rm{/d}}{{\rm{f}}_{{\rm{dumb}}}}}}。$ (15)

2 结果与分析 2.1 胸径、年龄和胸径、树高单木生物量模型及其比较

2.2 含有哑变量的单木地上生物量模型

2.3 含有哑变量的单木地上生物量各组分非线性联立方程组

3 结论与讨论