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金沟岭林场天然云冷杉林冠幅模型和估计方法比较

周泽宇 符利勇 张晓红 张会儒 雷相东

周泽宇, 符利勇, 张晓红, 张会儒, 雷相东. 金沟岭林场天然云冷杉林冠幅模型和估计方法比较[J]. 北京林业大学学报, 2021, 43(8): 29-40. doi: 10.12171/j.1000-1522.20210134
引用本文: 周泽宇, 符利勇, 张晓红, 张会儒, 雷相东. 金沟岭林场天然云冷杉林冠幅模型和估计方法比较[J]. 北京林业大学学报, 2021, 43(8): 29-40. doi: 10.12171/j.1000-1522.20210134
Zhou Zeyu, Fu Liyong, Zhang Xiaohong, Zhang Huiru, Lei Xiangdong. Comparison of crown width models and estimation methods of natural spruce fir forest in Jingouling Forest Farm of northeastern China[J]. Journal of Beijing Forestry University, 2021, 43(8): 29-40. doi: 10.12171/j.1000-1522.20210134
Citation: Zhou Zeyu, Fu Liyong, Zhang Xiaohong, Zhang Huiru, Lei Xiangdong. Comparison of crown width models and estimation methods of natural spruce fir forest in Jingouling Forest Farm of northeastern China[J]. Journal of Beijing Forestry University, 2021, 43(8): 29-40. doi: 10.12171/j.1000-1522.20210134

金沟岭林场天然云冷杉林冠幅模型和估计方法比较

doi: 10.12171/j.1000-1522.20210134
基金项目: 国家重点研发计划课题(2017YFC0504101)
详细信息
    作者简介:

    周泽宇,博士生。主要研究方向:森林生长收获预估模型。Email:zeyuzho@163.com 地址:100091 北京市海淀区香山路东小府1号中国林业科学研究院资源信息研究所

    责任作者:

    张会儒,研究员,博士生导师。主要研究方向:森林可持续经营。Email:huiru@ifrit.ac.cn 地址:102300北京市门头沟区水闸西路1号中国林业科学研究院华北林业实验中心

  • 中图分类号: S758.5

Comparison of crown width models and estimation methods of natural spruce fir forest in Jingouling Forest Farm of northeastern China

  • 摘要:   目的  对比不同冠幅预测方法对云冷杉幼树不同方向冠幅(东、西、南、北、东西、南北、平均冠幅)的预测精度的差异,为天然云冷杉林经营提供一定的理论依据。  方法  利用2013年金沟岭云冷杉3块1 hm2固定样地中云冷杉幼树各向冠幅实测数据,以逻辑斯蒂模型为基础模型,以非线性最小二乘法为基础方法进行模型初步拟合。以1/D、1/D0.5、1/D2作为模型的权函数进行模型异方差的消除。以不加权非线性似乎不相关法、加权非线性似乎不相关法、分位数回归法、非线性最小二乘法分别构建了云冷杉幼树冠幅各组分预测模型。  结果  模型拟合结果显示,分位数回归模型的拟合效果在云冷杉幼树冠幅预测模型中拟合精度最低;相较于分位数回归而言,加权非线性似乎不相关回归模型拟合效果与加权最小二乘模型拟合效果相当。模型拟合效果排序为:加权NSUR ≈ 加权OLS > OLS > QR。以1/D2作为模型的权函数时,模型残差图的异方差趋势被消除最明显,该权函数为最优权函数。  结论  本文中非线性分位数回归模型拟合效果不一定比非线性最小二乘法更好。加权NSUR模型(权函数为1/D2)可以为金沟岭林场云冷杉幼树冠幅的预测提供一定的理论基础。

     

  • 图  1  不同冠幅组分与胸径、树高之间关系图

    SCR:南冠幅South crown width;NCR:北冠幅North crown width;ECR:东冠幅 East crown width;WCR:西冠幅 West crown width;EWCW:东西冠幅 East-west crown width;SNCW:南北冠幅South-north crown width;CW:平均冠幅 Average crown width;DBH:胸径 DBH;H:树高Tree height. YLK-6、YLK-7、YLK-12分别代表云冷杉阔叶混交林第6号、7号、12号样地YLK-6,YLK-7,YLK-12 represent the 6th, 7th, 12th sample plots of spruce-fir broadleaved mixed forest

    Figure  1.  Relationship between different crown components and DBH, H

    图  2  基础模型拟合残差图

    Figure  2.  Fitted residual plot of base models

    图  3  加权模型拟合残差图

    Figure  3.  Fitted residual plot of weighted base models

    表  1  数据描述性统计分析

    Table  1.   Statistics of modeling data and validation data

    项目 Item变量 Variable最大值 Max.最小值 Min.均值 Mean标准差 Std.
    建模数据
    Model-fitting data (n = 548)
    胸径 DBH/cm 5.00 1.00 2.99 1.14
    树高 Tree height (H)/m 11.90 1.50 3.60 1.55
    南冠幅 South crown width (SCR)/m 2.96 0.29 1.08 0.44
    北冠幅 North crown width (NCR)/m 3.66 0.00 1.11 0.50
    西冠幅 West crown width (WCR)/m 3.23 0.00 1.13 0.51
    东冠幅 East crown width (ECR)/m 2.87 0.06 1.06 0.40
    南北冠幅 South-north crown width (SNCW)/m 5.35 0.61 2.19 0.80
    东西冠幅 East-west crown width (EWCW)/m 6.40 0.68 2.19 0.83
    平均冠幅 Average crown width (CW)/m 5.35 0.68 2.19 0.77
    检验数据
    Model-validation data (n = 235)
    胸径 DBH/cm 5.00 1.00 3.01 1.18
    树高 Tree height (H)/m 11.10 1.50 3.56 1.47
    南冠幅 South crown width (SCR)/m 2.90 0.00 1.05 0.45
    北冠幅 North crown width (NCR)/m 3.12 0.00 1.06 0.50
    西冠幅 West crown width (WCR)/m 3.06 0.33 1.13 0.51
    东冠幅 East crown width (ECR)/m 2.81 0.22 1.03 0.37
    南北冠幅 South-north crown width (SNCW)/m 5.26 0.99 2.16 0.80
    东西冠幅 East-west crown width (EWCW)/m 6.02 0.90 2.11 0.83
    平均冠幅 Average crown width (CW)/m 5.13 1.01 2.13 0.77
    下载: 导出CSV

    表  2  基础模型拟合指标统计

    Table  2.   Fitting results of basic models

    模型 Model$\overline e$R2RMSE
    CWS −0.000 3 0.298 3 0.369 8
    CWN −0.000 2 0.278 0 0.421 1
    CWE −0.000 2 0.309 8 0.329 3
    CWW −0.000 2 0.267 4 0.439 5
    CWEW −0.000 4 0.368 9 0.635 8
    CWSN −0.000 5 0.369 1 0.656 8
    CW −0.000 5 0.411 6 0.590 4
    下载: 导出CSV

    表  3  加入权函数后基础模型拟合指标统计

    Table  3.   Fitting index statistics of basic models by addition of weight function

    模型 Model1/D 1/D2 1/D0.5
    R2RMSER2RMSER2RMSE
    CWS 0.372 4 0.205 1 0.416 1 0.122 6 0.336 9 0.273 4
    CWN 0.342 4 0.233 2 0.368 7 0.140 2 0.312 7 0.310 8
    CWE 0.360 1 0.195 5 0.363 6 0.128 3 0.339 3 0.250 9
    CWW 0.345 4 0.244 0 0.382 2 0.147 4 0.309 0 0.324 9
    CWSN 0.446 0 0.361 4 0.471 7 0.225 5 0.411 9 0.475 0
    CWEW 0.444 0 0.365 4 0.479 7 0.219 5 0.409 4 0.486 4
    CW 0.492 5 0.331 0 0.527 5 0.201 0 0.455 9 0.439 1
    下载: 导出CSV

    表  4  可加性冠幅模型参数估计

    Table  4.   Parameter estimation of additivity crown model

    CWSCWNCWECWW
    参数
    Parameter
    估计值
    Estimation
    参数
    Parameter
    估计值
    Estimation
    参数
    Parameter
    估计值
    Estimation
    参数
    Parameter
    估计值
    Estimation
    a0 0.875 (0.112) b0 1.040 (0.184) c0 0.741 (0.102) d0 0.855 (0.133)
    a1 0.096 (0.018) b1 0.098 (0.022) c1 0.112 (0.018) d1 0.118 (0.021)
    a2 1.770 (0.352) b2 1.653 (0.324) c2 1.389 (0.423) d2 1.835 (0.421)
    a3 0.977 (0.237) b3 0.659 (0.188) c3 1.119 (0.378) d3 0.977 (0.265)
    注: 括号内的数值是标准差。Note: value in brackets is the standard deviation.
    下载: 导出CSV

    表  5  可加性冠幅模型拟合精度

    Table  5.   Fitting accuracy of additivity crown model

    评价指标 Evaluation indexCWSCWNCWECWWCWSNCWEWCW
    R2 0.416 1 0.368 8 0.363 7 0.382 3 0.479 5 0.471 6 0.527 3
    RMSE 0.122 6 0.140 2 0.128 3 0.147 4 0.219 5 0.225 6 0.201 0
    下载: 导出CSV

    表  6  参数估计的残差方差−协方差矩阵

    Table  6.   Variance-covariance matrix of parameter estimation

    CWSCWNCWECWWCWSNCWEWCW
    CWS 0.015 0 0.006 7 0.006 8 0.009 5 0.021 7 0.016 2 0.019 0
    CWN 0.006 7 0.019 6 0.005 9 0.008 6 0.026 4 0.014 6 0.020 5
    CWE 0.006 8 0.005 9 0.016 5 0.006 3 0.012 7 0.022 8 0.017 8
    CWW 0.009 5 0.008 6 0.006 3 0.021 7 0.018 1 0.028 0 0.023 1
    CWSN 0.021 7 0.026 4 0.012 7 0.018 1 0.048 2 0.030 9 0.039 6
    CWWE 0.016 2 0.014 6 0.022 8 0.028 0 0.030 9 0.050 9 0.041 0
    CW 0.019 0 0.020 5 0.017 8 0.023 1 0.039 6 0.041 0 0.040 4
    下载: 导出CSV

    表  7  不同分位数模型拟合统计结果

    Table  7.   Fitting results of various quantile crown models

    模型 Model分位数 Quantile (τ)$\overline e$R2RMSE
    CWS 0.3 0.189 4 0.083 8 0.422 5
    0.4 0.127 8 0.194 9 0.396 1
    0.5 0.041 4 0.287 2 0.372 7
    0.6 −0.028 2 0.293 8 0.371 0
    0.7 −0.147 4 0.167 2 0.402 9
    CWN 0.3 0.198 4 0.093 7 0.471 7
    0.4 0.124 4 0.204 0 0.442 1
    0.5 0.042 9 0.264 7 0.424 9
    0.6 −0.025 0 0.273 7 0.422 3
    0.7 −0.134 6 0.182 8 0.447 9
    CWE 0.3 0.164 6 0.106 3 0.374 7
    0.4 0.096 6 0.221 5 0.349 7
    0.5 0.019 7 0.282 6 0.335 7
    0.6 −0.063 3 0.278 5 0.336 7
    0.7 −0.148 2 0.159 0 0.363 5
    CWW 0.3 0.239 7 0.019 1 0.508 4
    0.4 0.153 4 0.163 0 0.469 7
    0.5 0.075 9 0.241 2 0.447 3
    0.6 −0.039 8 0.247 6 0.445 4
    0.7 −0.153 7 0.150 7 0.473 1
    CWSN 0.3 0.339 9 0.171 1 0.752 7
    0.4 0.211 4 0.287 7 0.697 8
    0.5 0.072 5 0.350 9 0.666 1
    0.6 −0.097 6 0.348 4 0.667 4
    0.7 −0.284 0 0.229 9 0.725 5
    CWEW 0.3 0.341 6 0.162 2 0.732 4
    0.4 0.229 9 0.267 2 0.685 0
    0.5 0.046 5 0.365 3 0.637 6
    0.6 −0.087 0 0.351 4 0.644 5
    0.7 −0.288 4 0.212 4 0.710 1
    CW 0.3 0.319 1 0.212 1 0.683 0
    0.4 0.209 9 0.321 6 0.633 9
    0.5 0.046 0 0.405 6 0.593 7
    0.6 −0.107 9 0.388 4 0.601 9
    0.7 −0.284 9 0.243 4 0.669 4
    下载: 导出CSV

    表  8  0.55分位数模型参数估计

    Table  8.   Parameter estimation at 0.55 tau

    参数 Parameter方法 MethodCWSCWNCWECWWCWSNCWEWCW
    a0 QR 1.177 1.573 1.469 1.191 4.386 2.195 2.561
    a1 QR 0.072 0.040 0.032 0.082 0.148 0.160 0.122
    a2 QR 1.748 2.422 2.048 1.988 3.363 1.912 2.115
    a3 QR 0.580 0.518 0.521 0.620 0.332 0.725 0.628
    注:QR为分位数回归。下同。Notes: QR is quantile regression. The same below.
    下载: 导出CSV

    表  9  0.55分位数回归模型拟合结果

    Table  9.   Fitting results of 0.55 quantile models

    模型 Model方法 Method$\overline e$R2RMSE
    CWS QR −0.000 9 0.298 3 0.369 8
    CWN QR −0.008 5 0.274 4 0.422 1
    CWE QR −0.025 9 0.295 4 0.332 7
    CWW QR 0.015 5 0.264 4 0.440 4
    CWSN QR −0.022 7 0.360 4 0.661 3
    CWEW QR −0.022 1 0.366 3 0.637 1
    CW QR −0.028 3 0.408 6 0.591 9
    下载: 导出CSV

    表  10  模型检验结果

    Table  10.   Validation results of models

    评价指标
    Evaluation index
    方法
    Method
    CWSCWNCWECWWCWSNCWEWCW
    $\overline e$ OLS −0.031 2 −0.050 0 −0.032 2 −0.000 2 −0.081 3 −0.032 5 −0.056 7
    加权OLS Weighted OLS −0.025 9 0.046 9 −0.027 3 0.002 7 −0.073 0 −0.024 8 −0.048 3
    加权NSUR Weighted NSUR −0.025 2 −0.046 2 −0.027 3 0.002 9 −0.071 4 −0.024 4 −0.047 9
    QR −0.031 9 −0.059 8 −0.060 4 0.014 7 −0.109 7 −0.054 3 −0.086 0
    R2 OLS 0.275 4 0.140 8 0.266 2 0.270 9 0.265 3 0.329 0 0.333 5
    加权OLS Weighted OLS 0.277 2 0.130 9 0.273 1 0.271 4 0.258 0 0.330 9 0.329 0
    加权NSUR Weighted NSUR 0.389 3 0.229 4 0.345 7 0.303 9 0.373 5 0.407 7 0.429 9
    QR 0.275 2 0.142 5 0.223 8 0.281 2 0.251 5 0.329 8 0.322 8
    RMSE OLS 0.385 6 0.462 5 0.320 7 0.435 8 0.714 6 0.658 3 0.630 5
    加权OLS Weighted OLS 0.385 1 0.465 1 0.319 1 0.435 6 0.718 1 0.657 4 0.632 7
    加权NSUR Weighted NSUR 0.121 6 0.166 6 0.121 9 0.159 1 0.243 2 0.233 3 0.219 8
    QR 0.385 6 0.462 0 0.329 8 0.432 7 0.721 2 0.657 9 0.635 6
    注 Notes:OLS:最小二乘法 Least square method;加权OLS:加权最小二乘法 Weighted least square method;加权NSUR:加权非线性似乎不相关回归 Weighted nonlinear seemingly unrelated regression.
    下载: 导出CSV
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出版历程
  • 收稿日期:  2021-04-12
  • 修回日期:  2021-05-26
  • 网络出版日期:  2021-06-10
  • 刊出日期:  2021-08-31

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