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利用分位数组合预测兴安落叶松枝下高

王君杰 姜立春

王君杰, 姜立春. 利用分位数组合预测兴安落叶松枝下高[J]. 北京林业大学学报, 2021, 43(3): 9-17. doi: 10.12171/j.1000-1522.20200075
引用本文: 王君杰, 姜立春. 利用分位数组合预测兴安落叶松枝下高[J]. 北京林业大学学报, 2021, 43(3): 9-17. doi: 10.12171/j.1000-1522.20200075
Wang Junjie, Jiang Lichun. Predicting height to crown base for Larix gmelinii using quantile groups[J]. Journal of Beijing Forestry University, 2021, 43(3): 9-17. doi: 10.12171/j.1000-1522.20200075
Citation: Wang Junjie, Jiang Lichun. Predicting height to crown base for Larix gmelinii using quantile groups[J]. Journal of Beijing Forestry University, 2021, 43(3): 9-17. doi: 10.12171/j.1000-1522.20200075

利用分位数组合预测兴安落叶松枝下高

doi: 10.12171/j.1000-1522.20200075
基金项目: 国家自然科学基金项目(31570624),黑龙江省应用技术研究与开发计划项目(GA19C006),中央高校基本科研业务费专项(2572019CP15), 黑龙江省头雁创新团队计划
详细信息
    作者简介:

    王君杰,博士生。主要研究方向:林分生长与收获模型。Email:wang.junjie521@qq.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:

    姜立春,教授,博士生导师。主要研究方向:林分生长与收获模型。Email:jlichun@nefu.edu.cn 地址:同上

  • 中图分类号: S757

Predicting height to crown base for Larix gmelinii using quantile groups

  • 摘要:   目的  本文使用分位数回归和分位数组合对枝下高进行建模和预测,为单木枝下高模型的构建提供新的思路和方法。  方法  利用大兴安岭新林区4个林场的兴安落叶松天然林实测数据,采用非线性回归构建枝下高基础和广义模型并分别扩展到分位数回归。使用三分位数组合($\tau {\text{ = }}$ 0.1, 0.5, 0.9)、五分位数组合($\tau {\text{ = }}$ 0.1, 0.3, 0.5, 0.7, 0.9)、九分位数组合($\tau {\text{ = }}$ 0.1, 0.2, 0.3, 0.4, 0.5, 0.6, 0.7, 0.8, 0.9)和4种抽样设计(抽最大树、抽最小树、抽平均木、随机抽取)进行预测,比较不同分位数组合的预测效果并分析不同抽样设计对预测精度的影响。同时使用双重交叉检验对非线性回归、最优位数回归和最优分位数组合进行比较。模型拟合和检验的评价指标主要包括平均绝对误差(MAE)、均方根误差(RMSE)、相对误差(MPE)和调整确定系数(${{R}}_{{\rm{adj}}}^2$)。  结果  (1)无论是非线性回归还是分位数回归,广义模型的拟合MAE较基础模型可降低6% ~ 12%,RMSE可降低6% ~ 10%,检验效果也优于基础模型。枝下高与胸径呈负相关、与样地优势高和每公顷断面积呈正相关。(2)中位数回归在所有分位数中拟合能力最好,且效果与非线性回归相似。分位数回归可以描述枝下高的分布。(3)3种分位数组合都可以对枝下高模型进行预测且效果相差不大,三分位数组合就可以满足枝下高的预测精度。中位数回归的交叉检验结果与非线性回归相似,三分位数组合的预测能力最优,MAE和MPE较非线性回归和中位数回归分别下降了20%和4%左右,${{R}}_{{\rm{adj}}}^2$提高了16%左右。(4)基础和广义分位数组合的最优抽样设计分别为抽平均木5株和抽大树7株。  结论  本研究基于三分位数组合($\tau {\text{ = }}$ 0.1, 0.5, 0.9)的枝下高模型可以提高预测精度,具体应用基础和广义分位数组合模型的最优抽样设计分别为抽平均木5株和抽大树7株。综合预测精度和调查成本的考虑,在实践中应用分位数组合时,推荐在样地中抽取5 株平均木对枝下高进行预测。

     

  • 图  1  非线性回归和基于5个分位点(0.1、0.3、0.5、0.7和0.9)的分位数回归的基础(A)和广义模型(B)的模拟曲线

    Figure  1.  Graphs of observed values (grey dots), simulation curves (grey curves) generated by the basic (A) and generalized nonlinear regression (B) and simulation curves (black curves) generated by the basic quantile regression (A) and generalized quantile regression (B) based on five quantiles (0.1, 0.3, 0.5, 0.7 and 0.9)

    图  2  广义模型的协变量对枝下高影响的模拟

    Figure  2.  Simulation on the effects of generalized model’s covariates on HCB

    图  3  分位数组合模型的预测误差比较

    a、e. 抽大树;b、f. 抽小树;c、g. 抽平均木;d、h. 随机抽取。a, e, the largest DBH sampling; b, f, the smallest DBH sampling; c, g, mean DBH sampling; d, h, random sampling.

    Figure  3.  Comparison of prediction errors of quantile groups

    表  1  落叶松天然林各样木调查因子数据统计

    Table  1.   Deseriptive statistics for Larix gmelinii sample trees

    变量 Variable组1 Group 1组2 Group 2
    平均值
    Mean value
    标准差
    SD
    最小值
    Min.
    最大值
    Max.
    平均值
    Mean value
    标准差
    SD
    最小值
    Min.
    最大值
    Max.
    树高 Total tree height (THT)/m 11.0 3.3 3.4 23.8 10.6 3.1 3.7 23.3
    枝下高 Height to crown base (HCB)/m 5.3 2.3 0.7 13.8 5.3 2.2 0.6 14.4
    胸径 Diameter at breast height (DBH)/cm 11.1 4.4 5.0 28.6 10.7 4.2 5.0 32.5
    优势高 Dominant height (HDOM)/m 15.9 2.4 11.1 19.7 15.6 2.3 11.3 22.0
    每公顷断面积/(m2·hm−2)
    Basal area per hectare (BA)/(m2·ha−1)
    17.9 8.6 4.5 37.5 18.1 7.0 2.9 31.7
    每公顷株数/(株·hm−2)
    Number of trees per hectare/(tree·ha−1)
    1 705.0 937.0 483.0 4 400.0 1 843.0 680.0 183.0 3 450.0
    下载: 导出CSV

    表  2  非线性回归和分位数回归的参数估计和拟合统计量

    Table  2.   Parameter estimation and fitting statistics for nonlinear regression and quantile regression at nine quantiles

    参数估计方法
    Parameter estimating method
    模型 Model${\;\beta _0}$${\;\beta _1}$${\;\beta _2}$${\;\beta _3}$${\;\beta _4}$平均绝对误差
    MAE/m
    均方根误差
    RMSE/m
    非线性回归
    Nonlinear regression
    基础模型 Basic model 0.238 6 −0.016 5 1.180 8 1.480 8
    广义模型 Generalized model 0.974 0 −0.045 6 0.045 1 −0.041 3 −0.014 3 1.066 1 1.366 0
    分位数回归
    Quantile regression
    基础模型 Basic model
    $\tau = 0.1$ 1.318 1 −0.040 6 2.139 0 2.545 3
    $\tau = 0.2$ 1.008 0 −0.039 9 1.629 2 1.983 7
    $\tau = 0.3$ 0.700 7 −0.031 9 1.351 6 1.666 6
    $\tau = 0.4$ 0.432 4 −0.023 3 1.218 6 1.514 8
    $\tau = 0.5$ 0.186 2 −0.014 4 1.179 3 1.482 0
    $\tau = 0.6$ −0.071 0 −0.005 6 1.220 0 1.557 2
    $\tau = 0.7$ −0.278 8 0.000 7 1.327 3 1.704 7
    $\tau = 0.8$ −0.541 0 0.008 9 1.542 8 1.959 2
    $\tau = 0.9$ −0.797 7 0.013 6 1.900 7 2.333 6
    广义模型 Generalized model
    $\tau = 0.1$ 1.998 3 −0.054 0 0.044 8 −0.054 5 −0.015 0 1.884 4 2.280 4
    $\tau = 0.2$ 1.732 9 −0.065 2 0.053 5 −0.049 6 −0.017 3 1.438 3 1.799 4
    $\tau = 0.3$ 1.494 7 −0.050 7 0.049 3 −0.052 8 −0.017 7 1.212 5 1.547 3
    $\tau = 0.4$ 1.239 8 −0.052 4 0.052 7 −0.050 4 −0.014 8 1.101 7 1.411 7
    $\tau = 0.5$ 1.023 3 −0.046 1 0.049 1 −0.048 2 −0.014 0 1.064 8 1.368 6
    $\tau = 0.6$ 0.725 8 −0.039 9 0.047 0 −0.043 6 −0.011 6 1.098 8 1.417 0
    $\tau = 0.7$ 0.528 0 −0.037 8 0.044 6 −0.041 1 −0.009 9 1.203 8 1.553 1
    $\tau = 0.8$ 0.250 2 −0.031 4 0.042 6 −0.037 4 −0.009 1 1.405 0 1.784 1
    $\tau = 0.9$ −0.131 6 −0.021 8 0.035 7 −0.028 0 −0.009 9 1.787 8 2.187 0
    下载: 导出CSV

    表  3  非线性回归、中位数回归和使用最优抽样设计的三分位数组合的交叉检验统计量

    Table  3.   Two-fold evaluation statistics of nonlinear regression, median quantile regression and three quantile groups using optimal sampling design

    参数估计方法
    Parameter estimating method
    模型
    Model
    平均绝对误差
    MAE/m
    均方根误差
    RMSE/m
    相对误差
    MPE/%
    ${{R}}_{\rm{adj}}^2$
    非线性回归
    Nonlinear regression
    基础模型
    Basic model
    1.187 7 1.490 2 22.488 6 0.565 4
    广义模型
    Generalized model
    1.079 4 1.382 4 20.436 9 0.625 1
    分位数回归
    Quantile regression
    基础中位数回归
    Basic median regression ($\tau = 0.5$)
    1.185 1 1.490 7 22.440 1 0.565 3
    广义中位数回归
    Generalized median regression ($\tau = 0.5$)
    1.082 0 1.388 4 20.486 6 0.621 9
    分位数组合
    Quantile group
    基础三分位数组合
    Basic three quantiles group ($\tau {{ = 0}}{\rm{.1,}}\;0.5,\;0.9$)
    0.958 9 1.317 8 18.154 8 0.659 4
    广义三分位数组合
    Generalized three quantile group ($\tau {{ = 0} }{\rm{.1,} }\;0.5,\;0.9$)
    0.854 7 1.188 4 16.183 3 0.723 1
    下载: 导出CSV
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出版历程
  • 收稿日期:  2020-03-18
  • 修回日期:  2020-04-14
  • 网络出版日期:  2021-03-19
  • 刊出日期:  2021-04-16

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