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黑龙江西部地区人工小黑杨立木可加性生物量模型

宋博 李凤日 董利虎 周翼飞

宋博, 李凤日, 董利虎, 周翼飞. 黑龙江西部地区人工小黑杨立木可加性生物量模型[J]. 北京林业大学学报, 2018, 40(11): 58-68. doi: 10.13332/j.1000-1522.20180062
引用本文: 宋博, 李凤日, 董利虎, 周翼飞. 黑龙江西部地区人工小黑杨立木可加性生物量模型[J]. 北京林业大学学报, 2018, 40(11): 58-68. doi: 10.13332/j.1000-1522.20180062
Song Bo, Li Fengri, Dong Lihu, Zhou Yifei. Additive system of biomass equations for planted Populus simonii × P. nigra in western Heilongjiang Province of northeastern China[J]. Journal of Beijing Forestry University, 2018, 40(11): 58-68. doi: 10.13332/j.1000-1522.20180062
Citation: Song Bo, Li Fengri, Dong Lihu, Zhou Yifei. Additive system of biomass equations for planted Populus simonii × P. nigra in western Heilongjiang Province of northeastern China[J]. Journal of Beijing Forestry University, 2018, 40(11): 58-68. doi: 10.13332/j.1000-1522.20180062

黑龙江西部地区人工小黑杨立木可加性生物量模型

doi: 10.13332/j.1000-1522.20180062
基金项目: 

本科生创新项目 201710225288

黑龙江省留学归国人员科学基金项目 LC2016007

国家自然科学基金青年项目 31600510

详细信息
    作者简介:

    宋博。主要研究方向:森林经理学。Email: 1286785656@qq.com  地址: 150040  黑龙江省哈尔滨市和兴路26号东北林业大学林学院

    责任作者:

    董利虎,博士,副教授。主要研究方向:林分生长与收获模型。Email: donglihu2006@163.com   地址:同上

  • 中图分类号: S718.55

Additive system of biomass equations for planted Populus simonii × P. nigra in western Heilongjiang Province of northeastern China

  • 摘要: 目的森林生物量和碳储量是研究许多林业问题与生态问题的基础。因此,准确测定生物量和碳储量十分重要。建立生物量模型是生物量和碳储量估测的重要手段。以人工小黑杨为研究对象,进行各分项生物量最优模型的选取,构建3种小黑杨可加性生物量模型系统,即基于胸径变量的一元可加性生物量模型系统、基于胸径和树高变量的二元可加性生物量模型系统以及基于最优变量的多元可加性生物量模型系统,为全国性生物量监测提供可靠的理论与技术支持。方法采用聚合型可加性模型来建立生物量模型;模型参数估计采用非线性似乎不相关回归模型方法;采用“刀切法”评价所建立的3种立木可加性生物量模型。结果仅含有胸径的异速生长方程是一种最为简单的模型形式,且具有较高的预测精度。包含树高和树冠属性因子(冠幅和冠长)的生物量模型能提高模型的预测能力,尤其能显著提高树枝、树叶和树冠生物量模型的预测能力。所建立的3种小黑杨可加性生物量模型拟合效果较好,其调整后确定系数(Ra2)均大于0.81,平均相对误差(ME)为-1.0%~10.0%,平均相对误差绝对值(MAE)均小于25%,所有模型的平均预测精度在85%以上。多元可加性生物量模型优于一元可加性生物量模型和二元可加性生物量模型。结论为了使模型参数估计更有效,所建立的生物量模型需要考虑立木总生物量及各分项生物量的可加性。虽然获取树冠属性因子需要花费大量人力和财力,但随着林地环境的变化,多元可加性生物量模型在结合生长模型精确估计小黑杨生物量方面具有一定的优势。总的来看,所建立的立木生物量模型均可对小黑杨生物量进行很好的估算。

     

  • 图  1  小黑杨树根、树干、树枝和树叶生物量与胸径、树高、冠幅和冠长的关系

    Figure  1.  Relationship between root, stem, branch, and foliage biomass of the sampled trees and DBH, tree height, crown width, and crown length for Populus simonii × P. nigra

    图  2  小黑杨不同径级3个可加性模型系统的检验结果

    Figure  2.  Validation of the three additive systems across diameter classes for planted Populus simonii × P. nigra

    表  1  小黑杨生物量统计

    Table  1.   Statistics of biomass of sampling trees for Populus simonii × P. nigra

    径级Diameter class/cm株数Plant numberD/cmH/mCW/mCL/mWr/kgWs/kgWb/kgWf/kg
    5≤D<10124.4~9.36.2~8.20.99~1.683.70~7.401.16~5.432.53~15.120.59~2.800.29~0.90
    10≤D<151410.1~14.89.6~11.91.26~2.133.70~8.305.37~15.6314.70~39.072.05~10.131.29~2.76
    15≤D<201015.2~20.011.6~13.51.75~2.315.90~9.0014.34~24.0635.05~72.468.84~19.112.93~4.68
    注:D为胸径,H为树高,CW为冠幅,CL为冠长;Wr为树根生物量,Ws为树干生物量,Wb为树枝生物量,Wf为树叶生物量。下同。Notes: D is diameter at breast height, H is tree height, CW is crown width, CL is crown length; Wr is root biomass, Ws is stem biomass, Wb is branch biomass, Wf is foliage biomass. The same below.
    下载: 导出CSV

    表  2  小黑杨各分项生物量备选模型形式

    Table  2.   Candidate model forms of root, stem, branch, and foliage biomass for planted Populus simonii × P. nigra

    模型类型Model type模型编号Model No.模型形式Model form
    一元One-variable 模型1 Model 1 $W_{i}=\beta_{i 0} D^{\beta_{i 1}}+\varepsilon_{i}$
    二元Two-variable模型2 Model 2$W_{i}=\beta_{i 0}\left(D^{2} H\right)^{\beta_{i 1}}+\varepsilon_{i}$
    模型3 Model 3$W_{i}=\beta_{i 0} D^{\beta_{i 1}} H^{\beta_{i 2}}+\varepsilon_{i}$
    多元Multiple-variable模型4 Model 4$W_{i}=\beta_{i 0} D^{\beta_{i 1}} H^{\beta_{i 2}} {\text{CW}}^{\beta_{i 3}}+\varepsilon_{i}$
    模型5 Model 5$W_{i}=\beta_{i 0} D^{\beta_{i 1}} H^{\beta_{i 2}} {\text{CL}}^{\beta_{i 3}}+\varepsilon_{i}$
    模型6 Model 6$W_{i}=\beta_{i 0} D^{\beta_{i 1}} H^{\beta_{i 2}} {\text{CW}}^{\beta_{i 3}} {\text{CL}}^{\beta_{i 4}}+\varepsilon_{i}$
    下载: 导出CSV

    表  3  小黑杨各分项生物量备选模型拟合优度统计量

    Table  3.   Goodness-of-fit statistics of the candidate model forms of root, stem, branch, and foliage biomass for planted Populus simonii × P. nigra

    各分项Component模型编号Model No.模型形式Model formRa2RMSE/kgAIC
    树根Root模型1 Model 1$W_{i}=\beta_{i 0} D^{\beta_{i 1}}+\varepsilon_{i}$0.977 01.10109.80
    模型2 Model 2$W_{i}=\beta_{i 0}\left(D^{2} H\right)^{\beta_{i 1}}+\varepsilon_{i}$0.968 81.28120.60
    模型3 Model 3$W_{i}=\beta_{i 0} D^{\beta_{i 1}} H^{\beta_{i 2}}+\varepsilon_{i}$0.977 51.09110.10
    模型4 Model 4$W_{i}=\beta_{i 0} D^{\beta_{i 1}} H^{\beta_{i 2}} {\text{CW}}^{\beta_{i 3}}+\varepsilon_{i}$0.976 81.10112.00
    模型5 Model 5$W_{i}=\beta_{i 0} D^{\beta_{i 1}} H^{\beta_{i 2}} {\text{CL}}^{\beta_{i 3}}+\varepsilon_{i}$0.976 81.10112.10
    模型6 Model 6$W_{i}=\beta_{i 0} D^{\beta_{i 1}} H^{\beta_{i 2}} {\text{CW}}^{\beta_{i 3}} {\text{CL}}^{\beta_{i 4}}+\varepsilon_{i}$0.976 11.12113.90
    树干Stem模型1 Model 1$W_{i}=\beta_{i 0} D^{\beta_{i 1}}+\varepsilon_{i}$0.978 32.69172.50
    模型2 Model 2$W_{i}=\beta_{i 0}\left(D^{2} H\right)^{\beta_{i 1}}+\varepsilon_{i}$0.988 91.92149.00
    模型3 Model 3$W_{i}=\beta_{i 0} D^{\beta_{i 1}} H^{\beta_{i 2}}+\varepsilon_{i}$0.991 51.69140.70
    模型4 Model 4$W_{i}=\beta_{i 0} D^{\beta_{i 1}} H^{\beta_{i 2}} {\text{CW}}^{\beta_{i 3}}+\varepsilon_{i}$0.991 21.71143.00
    模型5 Model 5$W_{i}=\beta_{i 0} D^{\beta_{i 1}} H^{\beta_{i 2}} {\text{CL}}^{\beta_{i 3}}+\varepsilon_{i}$0.991 71.66140.70
    模型6 Model 6$W_{i}=\beta_{i 0} D^{\beta_{i 1}} H^{\beta_{i 2}} {\text{CW}}^{\beta_{i 3}} {\text{CL}}^{\beta_{i 4}}+\varepsilon_{i}$0.991 41.59142.60
    树枝Branch模型1 Model 1$W_{i}=\beta_{i 0} D^{\beta_{i 1}}+\varepsilon_{i}$0.816 62.19158.10
    模型2 Model 2$W_{i}=\beta_{i 0}\left(D^{2} H\right)^{\beta_{i 1}}+\varepsilon_{i}$0.792 22.33162.50
    模型3 Model 3$W_{i}=\beta_{i 0} D^{\beta_{i 1}} H^{\beta_{i 2}}+\varepsilon_{i}$0.843 22.02153.50
    模型4 Model 4$W_{i}=\beta_{i 0} D^{\beta_{i 1}} H^{\beta_{i 2}} {\text{CW}}^{\beta_{i 3}}+\varepsilon_{i}$0.886 11.72143.20
    模型5 Model 5$W_{i}=\beta_{i 0} D^{\beta_{i 1}} H^{\beta_{i 2}} {\text{CL}}^{\beta_{i 3}}+\varepsilon_{i}$0.860 81.91150.20
    模型6 Model 6$W_{i}=\beta_{i 0} D^{\beta_{i 1}} H^{\beta_{i 2}} {\text{CW}}^{\beta_{i 3}} {\text{CL}}^{\beta_{i 4}}+\varepsilon_{i}$0.908 11.55136.50
    树叶Foliage模型1 Model 1$W_{i}=\beta_{i 0} D^{\beta_{i 1}}+\varepsilon_{i}$0.875 50.4446.10
    模型2 Model 2$W_{i}=\beta_{i 0}\left(D^{2} H\right)^{\beta_{i 1}}+\varepsilon_{i}$0.871 90.4548.10
    模型3 Model 3$W_{i}=\beta_{i 0} D^{\beta_{i 1}} H^{\beta_{i 2}}+\varepsilon_{i}$0.871 60.4547.10
    模型4 Model 4$W_{i}=\beta_{i 0} D^{\beta_{i 1}} H^{\beta_{i 2}} {\text{CW}}^{\beta_{i 3}}+\varepsilon_{i}$0.874 00.4448.30
    模型5 Model 5$W_{i}=\beta_{i 0} D^{\beta_{i 1}} H^{\beta_{i 2}} C L^{\beta_{i 3}}+\varepsilon_{i}$0.885 80.4244.90
    模型6 Model 6$W_{i}=\beta_{i 0} D^{\beta_{i 1}} H^{\beta_{i 2}} {\text{CW}}^{\beta_{i3}} {\text{CL}}^{\beta_{i 4}}+\varepsilon_{i}$0.887 10.4245.30
    下载: 导出CSV

    表  4  小黑杨3个可加性模型系统的参数估计值、拟合优度、权函数和怀特检验值

    Table  4.   Coefficient estimate, goodness-of-fit statistics, weight functions and White test of three additive systems for planted Populus simonii × P. nigra

    模型系统
    Model system
    各分项
    Component
    模型参数
    Model parameter
    Ra2RMSE权函数
    Weight function
    怀特检验P
    White test P value
    βi0 βi1 βi2 βi3 βi4
    模型系统1MS-1树根Root-3.250 82.188 50.9781.09D2.661 00.47
    树干Stem-3.721 81.513 81.325 80.9921.68D1.735 60.78
    树枝Branch-1.989 42.013 6-1.356 91.338 70.602 90.9151.49D4.777 70.35
    树叶Foliage-4.797 51.575 10.287 90.402 00.8930.41D1.877 00.48
    树冠Crown0.9241.74D4.787 40.42
    地上Aboveground0.9882.65D3.775 90.42
    总量Total0.9913.04D2.699 80.42
    模型系统2MS-2树根Root-3.186 92.166 30.9781.08D2.661 00.44
    树干Stem-2.306 72.187 70.9782.69D2.535 70.46
    树枝Branch-4.047 92.277 60.8152.18D6.360 10.59
    树叶Foliage-4.287 21.934 80.8780.43D4.440 10.57
    树冠Crown0.8482.45D5.724 70.79
    地上Aboveground0.9813.34D2.640 50.72
    总量Total0.9873.61D3.925 30.26
    模型系统3MS-3树根Root-3.060 02.303 8-0.202 00.9781.08D2.708 50.28
    树干Stem-3.675 91.516 41.303 60.9911.70D2.262 50.89
    树枝Branch-3.352 52.994 3-1.071 00.8402.04D3.404 30.67
    树叶Foliage-4.309 51.929 90.018 30.8790.44D2.440 40.35
    树冠Crown0.8612.34D4.170 70.92
    地上Aboveground0.9833.12D3.213 50.87
    总量Total0.9873.53D2.766 40.91
    下载: 导出CSV

    表  5  小黑杨3个可加性模型系统的检验结果

    Table  5.   Validation of the three additive systems for planted Populus simonii × P. nigra

    各分项Component平均相对误差Mean relative error (ME)平均相对误差绝对值Mean absolute relative error (MAE)平均预估误差Mean prediction error (MPE)
    模型系统1MS-1模型系统2MS-2模型系统3MS-3模型系统1MS-1模型系统2MS-2模型系统3MS-3模型系统1MS-1模型系统2MS-2模型系统3MS-3
    总量Total0.140.570.785.936.556.562.472.912.89
    地上生物量Aboveground biomass0.170.470.716.086.846.782.853.533.33
    树根生物量Root biomass1.232.312.1310.7811.0311.364.024.074.34
    树干生物量Stem biomass0.690.250.835.768.775.912.393.722.39
    树枝生物量Branch biomass-0.689.495.4416.5224.9023.259.5913.5712.62
    树叶生物量Foliage biomass3.804.866.4118.1819.2220.128.498.809.06
    树冠生物量Crown biomass-0.466.504.1614.3919.9018.638.5211.6111.01
    下载: 导出CSV
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  • 收稿日期:  2018-02-26
  • 修回日期:  2018-10-09
  • 刊出日期:  2018-11-01

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