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基于抚育间伐效应的红松人工林枝条密度模型

贾炜玮 罗天泽 李凤日

贾炜玮, 罗天泽, 李凤日. 基于抚育间伐效应的红松人工林枝条密度模型[J]. 北京林业大学学报, 2021, 43(2): 10-21. doi: 10.12171/j.1000-1522.20200057
引用本文: 贾炜玮, 罗天泽, 李凤日. 基于抚育间伐效应的红松人工林枝条密度模型[J]. 北京林业大学学报, 2021, 43(2): 10-21. doi: 10.12171/j.1000-1522.20200057
Jia Weiwei, Luo Tianze, Li Fengri. Branch density model for Pinus koraiensis plantation based on thinning effects[J]. Journal of Beijing Forestry University, 2021, 43(2): 10-21. doi: 10.12171/j.1000-1522.20200057
Citation: Jia Weiwei, Luo Tianze, Li Fengri. Branch density model for Pinus koraiensis plantation based on thinning effects[J]. Journal of Beijing Forestry University, 2021, 43(2): 10-21. doi: 10.12171/j.1000-1522.20200057

基于抚育间伐效应的红松人工林枝条密度模型

doi: 10.12171/j.1000-1522.20200057
基金项目: 国家自然科学基金面上项目(31870622),中央高校基本科研业务费专项(2572019CP08)
详细信息
    作者简介:

    贾炜玮,教授,博士生导师。主要研究方向:林分生长与收获模型。Email:jiaww2002@163.com 地址:150040 黑龙江省哈尔滨市香坊区和兴路26号东北林业大学林学院

    责任作者:

    李凤日,教授,博士生导师。主要研究方向:林分生长与收获模型。Email:fengrili@126.com 地址:同上

  • 中图分类号: S753.7

Branch density model for Pinus koraiensis plantation based on thinning effects

  • 摘要:   目的  分析抚育间伐对红松人工林枝条数量的影响,建立基于间伐效应的生物数学模型,为制定更加科学合理的间伐体制提供理论依据。  方法  基于黑龙江省林口林业局和东京城林业局不同林分条件及抚育间伐强度下的红松人工林49株解析木4 370组枝解析数据,利用R语言的nlme包,建立了基于抚育间伐效应的枝条密度单水平非线性混合模型,并利用调整决定系数($ {R}_{{\rm{a}}}^{2} $)、赤池信息准则(AIC)、贝叶斯信息准则(BIC)、对数似然值(Log-likelihood)以及似然比检验(LRT)等评价指标对所收敛的模型进行评价。  结果  当地位指数和树木等级相近时,抚育间伐强度和冠长越大,枝条密度越大;当抚育间伐强度和树木等级相近时,地位指数和冠长越大,枝条密度越大;而抚育间伐强度和地位指数相近时,树木胸径与枝条密度呈负相关。基于样地效应的混合模型模拟精度均高于基础模型和基于样木效应的混合模型,最终选用含有总着枝深度(DINC)、相对着枝深度的自然对数(lnRDINC)、相对着枝深度的平方(RDINC2)、胸径(DBH)、抚育间伐强度与间伐年龄的比值(TI/TA)这5个随机效应参数的非线性混合模型为枝条密度最优预测模型,其${R}_{{\rm{a}}}^{2}$为0.825 7,均方根误差(RMSE)为2.171 4。  结论  基于抚育间伐效应的红松枝条密度最优非线性混合效应模型,不但能提高模型精度,还能更加准确地体现抚育间伐对林木枝条产生的影响。

     

  • 图  1  红松人工林数据采样点位置分布

    Figure  1.  Location distribution of sampling points of Pinus koraiensis plantation

    图  2  最优基础模型和最优混合模型残差图

    Figure  2.  Residual plots of the best basic and mixed models

    图  3  不同条件下的枝条密度分布规律图

    Figure  3.  Distribution patterns of branch density under different conditions

    表  1  红松人工林抚育间伐因子及林分因子统计表

    Table  1.   Statistics of thinning and stand factors for Pinus koraiensis planation

    统计量
    Statistic
    间伐强度
    Thinning intensity
    (TI)/%
    间伐年龄/a
    Thinning age
    (TA)/year
    地位指数
    Site index
    (SI)/m
    林分平均胸径
    Average stand
    DBH/cm
    林分平均高
    Mean stand
    height/m
    林分断面积/(m2∙hm−2)
    Stand basal area/
    (m2∙ha−1)
    林分密度/(株∙hm−2)
    Stand density/
    (tree∙ha−1)
    最大值 Max. value 40.00 35.00 16.19 18.76 11.85 33.62 2 217
    最小值 Min. value 0.00 28.00 9.15 11.62 6.90 12.55 716
    平均值 Mean value 22.62 31.52 13.35 14.76 9.78 23.12 1 388
    标准差 SD 13.26 1.53 1.65 1.83 1.31 5.27 371
    变异系数 CV/% 58.64 4.84 12.38 12.40 13.37 22.79 26.72
    下载: 导出CSV

    表  2  红松人工林解析木和枝条分布统计表

    Table  2.   Statistics of sample trees and branch distribution for Pinus koraiensis planation

    项目
    Item
    统计量
    Statistic
    年龄/a
    Age/year
    胸径
    DBH/cm
    树高
    Tree height
    (HT)/m
    冠长
    Crown length
    (CL)/m
    冠幅
    Crown width
    (CW)/m
    冠长率
    Crown length
    ratio (CR)
    枝条密度/(个∙m−1
    Branch density/
    (number∙m−1)
    拟合数据
    (样本容量 = 40)
    Fitting data
    (sample size = 40)
    最大值 Max. value 38 23.60 14.23 10.60 2.93 0.88 29
    最小值 Min. value 31 8.00 7.05 4.30 1.13 0.48 1
    平均值 Mean value 35.15 14.79 10.42 6.96 1.97 0.68 13.98
    标准差 SD 1.53 4.60 1.79 1.34 0.45 0.11 5.20
    变异系数 CV/% 4.35 31.09 17.17 19.24 22.80 16.40 37.23
    检验数据
    (样本容量 = 9)
    Validation data
    (sample size = 9)
    最大值 Max. value 37 25.50 13.37 8.69 3.13 0.82 31
    最小值 Min. value 33 8.00 7.90 3.80 1.13 0.48 3
    平均值 Mean value 34.96 16.09 10.84 7.69 2.22 0.71 14.17
    标准差 SD 1.18 4.94 1.48 1.43 0.63 0.11 5.70
    变异系数 CV/% 3.38 30.67 13.67 18.55 28.48 15.21 40.21
    下载: 导出CSV

    表  3  不同间伐强度、不同地位指数枝条密度双因素方差分析

    Table  3.   Two-way ANOVA of different thinning intensities and site index for branch density

    TISIn总活枝数量
    Total number of
    living branch
    平均活枝密度/(个∙m−1)
    Average density of
    living branch/
    (number∙m−1)
    最大活枝密度/(个∙m−1)
    Max. density of
    living branch/
    (number∙m−1)
    最大活枝密度的冠层深度
    Crown depth of
    Max. branch
    density/m
    最大活枝密度相对冠层深度
    Relative crown depth of
    Max. branch
    density/%
    CK698 ± 33abcd14.1 ± 1.84ab19.59 ± 1.87ab2.76 ± 0.48bc41.97 ± 11.50b
    373 ± 21d12.3 ± 0.63ab16.09 ± 1.16bc2.99 ± 0.25abc55.27 ± 24.59ab
    V374 ± 7cd11.61 ± 0.35b16.21 ± 0.21bc4.14 ± 0.42a70.6 ± 2.4a
    L4108 ± 22abc13.9 ± 0.95ab23.51 ± 5.64a3.53 ± 0.79ab49.25 ± 8.6b
    272 ± 6d11.16 ± 0.29b16.56 ± 3.36bc1.90 ± 0.06c33 ± 5.23b
    V268 ± 1d11.39 ± 0.19b17.08 ± 0.8bc3.46 ± 0.77abc56.8 ± 14.01ab
    M10112 ± 15ab14.52 ± 3.06a19.34 ± 4.1b3.34 ± 1.04abc44.95 ± 14.29b
    797 ± 29abcd12.03 ± 1.91b15.9 ± 2.34c2.99 ± 1.35abc39.4 ± 14.89b
    V274 ± 21cd12.28 ± 3.5ab17.11 ± 2.43bc2.64 ± 0.43bc44.35 ± 6.15b
    H2132 ± 5a15.5 ± 0.68a21.51 ± 1.54ab2.88 ± 0.05abc34.1 ± 0.42b
    4119 ± 8a14.97 ± 0.81a20.15 ± 0.72ab3.44 ± 0.88abc48.5 ± 15.41b
    487 ± 34bcd13.68 ± 2.99ab17.44 ± 4.7bc3.04 ± 0.29abc50.8 ± 14.28ab
    注:n.解析木株数;地位指数等级(SI):Ⅰ (15.03 ~ 16.19 m)、Ⅱ (14.01 ~ 14.81 m)、Ⅲ (13.15 ~ 13.99 m)、Ⅳ (11.94 ~ 12.91 m)、Ⅴ (9.15 ~ 11.09 m)。表中数值为平均值 ± 标准差,同一列数据后不同字母表示5%水平差异显著。Notes: n represents parse tree number; site index level (SI): Ⅰ (15.03−16.19 m), Ⅱ (14.01−14.81 m), Ⅲ (13.15−13.99 m), Ⅳ (11.94−12.91 m), Ⅴ (9.15−11.09 m). The data in table are mean ± SD. Different letters in the same column after data indicate significant differences at 5% level.
    下载: 导出CSV

    表  4  最优基础模型参数拟合结果

    Table  4.   Fitting results of the best basic model

    参数 Parameter样本容量 Sample size估计值 Estimation标准误差 SEtP
    $\lambda $3 53424.485 5171.193 71320.512 1 < 0.000 1
    ${k_1}$3 5340.155 0000.012 95411.965 6 < 0.000 1
    ${k_2}$3 534−0.616 2050.017 812−34.595 3 < 0.000 1
    ${k_3}$3 5341.279 1260.062 99720.304 6 < 0.000 1
    ${k_4}$3 5340.005 2370.001 4033.733 7 < 0.000 1
    ${k_5}$3 534−0.037 5610.006 627−5.667 9 < 0.000 1
    ${k_6}$3 534−0.048 6520.003 168−15.660 0 < 0.000 1
    ${k_7}$3 534−0.055 8320.005 951−9.381 7 < 0.000 1
    下载: 导出CSV

    表  5  基于不同随机效应参数组合的枝条密度模型拟合精度比较

    Table  5.   Comparison of mixed branch density model based on different random effect parameters

    随机效应
    Random effect
    模型
    Model
    随机效应参数
    Random effect
    parameter
    参数个数
    Number of
    parameter
    Ra 2AICBICLog-
    likelihood
    似然比检验
    Likelihood ratio
    test (LRT)
    P
    11无 None80.591 618 533.2918 588.82−9 257.64
    样木效应
    Sample tree effect
    11.1${k_3}$90.613 118 446.2318 507.91−9 213.1289.04 < 0.001
    11.2${k_3}$${k_7}$110.629 618 300.3718 374.38−9 138.18149.88 < 0.001
    11.3${k_1}$${k_4}$${k_5}$140.640 218 245.3518 337.87−9 107.6761.02 < 0.001
    样地效应
    Sample plot effect
    11.4${k_5}$90.675 017 910.1017 971.78−8 945.05
    11.5${k_2}$${k_4}$110.742 417 202.3917 276.40−8 589.19711.72 < 0.001
    11.6${k_1}$${k_2}$${k_4}$140.797 816 566.7816 659.30−8 268.39641.60 < 0.001
    11.7${k_1}$${k_2}$${k_4}$${k_7}$180.808 216 316.1816 433.37−8 139.09258.60 < 0.001
    11.8${k_1}$${k_2}$${k_3}$${k_4}$${k_7}$230.825 716 125.7116 273.74−8 038.85200.48 < 0.001
    下载: 导出CSV

    表  6  不同参数数量模型方差组成、参数估计及拟合统计量

    Table  6.   Variance component, fixed parameters and fitting statistic estimates of models with different numbers of parameters

    项目 Item参数 Parameter模型11 Model 11模型11.3 Model 11.3模型11.8 Model 11.8
    固定效应参数
    Fixed effect parameter
    $\lambda $24.485 5***25.595 1***22.221 1**
    ${k_1}$0.155 0***0.229 0***0.157 7
    ${k_2}$−0.616 2***−0.701 5***−0.656 9***
    ${k_3}$1.279 1***1.019 4***1.598 9***
    ${k_4}$0.005 2***−0.020 7**0.001 7
    ${k_5}$−0.037 6***−0.060 6***−0.100 8***
    ${k_6}$−0.048 7***−0.026 7***−0.050 1*
    ${k_7}$−0.055 8***−0.002 7−0.350 5*
    随机效应方差−协方差结构
    Variance of random effect-covariance structure
    $\sigma _{{k_1}}^2$0.050 50.207 6
    $\sigma _{{k_2}}^2$0.183 8
    $\sigma _{{k_3}}^2$0.886 5
    $\sigma _{{k_4}}^2$0.016 00.048 3
    $\sigma _{{k_5}}^2$0.046 3
    $\sigma _{{k_7}}^2$0.313 3
    $\sigma _{{k_1}{k_2}}^2$−0.915 0
    $\sigma _{{k_1}{k_3}}^2$−0.936 0
    $\sigma _{{k_1}{k_4}}^2$0.105 0−0.911 0
    $\sigma _{{k_1}{k_5}}^2$−0.580 0
    $\sigma _{{k_1}{k_7}}^2$0.119 0
    $\sigma _{{k_2}{k_3}}^2$0.789 0
    $\sigma _{{k_2}{k_4}}^2$0.843 0
    $\sigma _{{k_2}{k_7}}^2$0.013 0
    $\sigma _{{k_3}{k_4}}^2$0.798 0
    $\sigma _{{k_3}{k_7}}^2$−0.085 0
    $\sigma _{{k_4}{k_5}}^2$−0.791 0
    $\sigma _{{k_4}{k_7}}^2$−0.471 0
    拟合统计量
    Fitting statistics
    $R_{\rm{a}}^2$0.591 60.640 20.825 7
    RMSE2.990 43.120 72.171 4
    注:***表示在P < 0.001水平上显著,**表示P < 0.01水平上显著,*表示P < 0.05水平上显著。Notes: *** represents significiance at P < 0.001 level; ** represents significiance P < 0.01 level; * represents significiance at P < 0.05 level.
    下载: 导出CSV

    表  7  最优基础模型与最优混合模型检验结果

    Table  7.   Validation results of the best basic model and the best mixed-effects model

    模型 Model样本容量 Sample size平均绝对偏差 MAE平均相对偏差绝对值 RMAE预估精度 Fp
    基础模型11 Basic model 118364.099 939.8697.376 4
    混合模型11.8 Mixed model 11.88362.465 420.8698.553 5
    下载: 导出CSV
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出版历程
  • 收稿日期:  2020-03-02
  • 修回日期:  2020-04-17
  • 网络出版日期:  2021-01-26
  • 刊出日期:  2021-02-24

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