高级检紡/a>

留言松/h2>

尊敬的读者、作者、审稿人, 关于本刊的投稿、审稿、编辑和出版的任何问? 您可以本页添加留言。我们将尽快给您答复。谢谢您的支?

姓名
邮箱
手机号码
标题
留言内容
验证?/th>

基于林木分级的大兴安岭天然兴安落叶松树高曲线研究

董灵泡/a>,邵威?/a>,田栋兂/a>,刘兆则/a>

downloadPDF
董灵? 邵威? 田栋? 刘兆? 基于林木分级的大兴安岭天然兴安落叶松树高曲线研究[J]. 北京林业大学学报. doi: 10.12171/j.1000-1522.20210513
引用本文: 董灵? 邵威? 田栋? 刘兆? 基于林木分级的大兴安岭天然兴安落叶松树高曲线研究[J]. 北京林业大学学报.doi:10.12171/j.1000-1522.20210513
shu
Dong Lingbo, Shao Weiwei, Tian Dongyuan, Liu Zhaogang. Height curve of natural Larix gmelinii in the Daxing’anling Mountains of northeastern China based on forest classification[J]. Journal of Beijing Forestry University. doi: 10.12171/j.1000-1522.20210513
Citation: Dong Lingbo, Shao Weiwei, Tian Dongyuan, Liu Zhaogang. Height curve of naturalLarix gmeliniiin the Daxing’anling Mountains of northeastern China based on forest classification[J].Journal of Beijing Forestry University.doi:10.12171/j.1000-1522.20210513
shu
doi:10.12171/j.1000-1522.20210513

  • 东北林业大学林学院森林生态系统可持续经营教育部重点实验室，黑龙江 哈尔 150040

基金项目:国家重点研发计划课题?022YFD2200502），中央高校基本科研业务费专项（2572022CG07），黑龙江头雁创新团队计划项目（森林资源高效培育技术研发团队）
详细信息
    作者简今

    董灵波，副教授。主要研究方向：森林可持续经营。Email９a href="//www.inggristalk.com/j/article/doi/10.12171/mailto:farrell0503@126.com">farrell0503@126.com　地址?50040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

    责任作耄

    刘兆刚，教授，博士生导师。主要研究方向：森林可持续研究。Email９a href="//www.inggristalk.com/j/article/doi/10.12171/mailto:lzg19700602@163.com">lzg19700602@163.com　地址：同三/span>

  • 中图分类叶S791.222；S750

Height curve of naturalLarix gmeliniiin the Daxing’anling Mountains of northeastern China based on forest classification

摘要
  • 摘要: 目的基于林木分级构建大兴安岭地区兴安落叶松的树高曲线模型，为该地区兴安落叶松的生长规律提供理论依据及森林可持续经营提供技术支撑、/sec> 方法以大兴安岭地区翠岗林?6块固定样地数据为基础，根据单木相对直径（ d）把林木分为了优势木、平均木、被压木3个等级，依据调整决定系数＇i>R 2 adj）最大、均方根误差（RMSE）和赤池信息量（AIC）最小的标准筛选出天然兴安落叶松各等级林木的最优树高曲线基础模型，并进一步评价和比较分位数回归和哑变量回归对兴安落叶松不同等级林木树高曲线模型模拟精度的影响、/sec> 结果天然兴安落叶松树高曲线的最优基础模型均为Wykoff方程；当将林分分级哑变量同时添加在Wykoff方程的参?i>a咋i>b上时，模型的拟合效果最?其中兴安落叶松树高曲线模型的调整系数＇i>R 2 adj）、均方根误差（RMSE）和赤池信息量（AIC）分别为0.858 8?.642 4? 081.902；兴安落叶松中的不同等级林木对应的最优分位数模型与林分整体无差别，均表现为中位数模型最优（卲i>τ= 0.5），其树高曲线的3个统计量则依次为0.849 8?.693 8? 211.037。经过比较分析可知，以林木分级为哑变量的树高曲线模型拟合效果最好、/sec> 结论含林木分级哑变量的大兴安岭兴安落叶松的树高曲线模型拟合效果优于基础模型，并且具有较好的预测精度和适应性，能反映不同林木等级下的树高、胸径的生长差异，可以为大兴安岭地区兴安落叶松的经营和生长预估提供理论依据、/sec>

    Abstract: ObjectiveThe tree height curve of main tree species was established based on tree classification, which provided reference for studying the growth law of Larix gmelinii, and provided technical support for forest sustainable management in Daxing’anling Mountains of northeastern China. MethodBased on the data of 56 fixed sample plots in Cuigang Forest farm of Daxing’anling Mountains, trees were divided into three grades of dominant, average and crushed trees according to the relative diameter ( d) of individual trees. Based on the maximum adjusted coefficient ( R 2 adj), minimum root mean square error (RMSE) and the minimum red pool information (AIC), the optimal tree height curve basic model of different grades of natural Larix gmeliniiwas screened out, and the effects of quantile regression and dummy variable regression on the simulation accuracy of tree height curve models of different grades of Larix gmeliniiwere further evaluated and compared. ResultThe optimal basic model of Larix gmeliniiheight curves was Wykoff equation. When the dumb variables of stand classification were added to parameters a and b of Wykoff equation, the model had the best fitting effect. R 2 adj, RMSE and AIC of Larix gmeliniitree species curve model were 0.858 8, 1.642 4 and 2 081.902, respectively. There was no difference between the optimal quantile model and the whole stand of Larix gmelinii, and the median model was optimal ( τ= 0.5). The three statistics of height curve of the deciduous pine were 0.849 8, 1.693 8 and 2 211.037, respectively. Through comparative analysis, the tree height curve model with tree classification as dummy variable had the best fitting effect. ConclusionThe height curve model of Larix gmeliniiin the Daxing’anling Mountains, which contains dummy variables for tree classification, has better fitting performance than the basic model, and has good prediction accuracy and adaptability. It can reflect the growth differences of tree height and DBH under different tree grades, and can provide a theoretical basis for the management and growth prediction of Larix gmeliniiin the Daxing’anling Mountains region.

    • HTML全文

  • ?nbsp; 1不同林木等级的兴安落叶松残差分布

    Figure 1.Residual distribution ofLarix gmeliniiunder different tree grades

    下载: 全尺寸图牆/a> 幻灯牆/a>

    ?nbsp; 2不同分位数兴安落叶松树高−胸径曲线模拞/p>

    Figure 2.Tree height-DBH curve simulation ofLarix gmeliniibased on base model, median model and different quantile groups

    下载: 全尺寸图牆/a> 幻灯牆/a>

    ?nbsp; 3基于林木分级的哑变量模型模拟曲线

    Figure 3.Dummy variable model simulation curve based on forest classification

    下载: 全尺寸图牆/a> 幻灯牆/a>

    ?nbsp; 1样地基本特征

    Table 1.Basic characteristics of the sample plots

    落叶松蓄积占毓br/>Percentage of larch volume 样地数量
    Number of sample plot    		 变量
    Variable    		 最小倻br/>Min. value 最大倻br/>Max. value 平均倻br/>Mean 标准?br/>SD 变异系数
    CV/%
    70%以上
    More than 70%    		 29 胸径 Diameter at breast height (D)/cm 9.9 20.5 12.9 2.3 18.1
    树高Tree height (H)/m 9.5 16.3 11.8 1.6 13.3
    林分密度/（株·hm?（br/>Stand density/(tree·ha?) 533.0 2 217.0 1 405.6 442.1 31.5
    50% ~ 70% 17 D/cm 9.7 15.9 12.2 1.6 13.5
    H/m 10.0 15.3 11.9 1.5 12.3
    林分密度/（株·hm?（br/>Stand density/(tree·ha?) 850.0 2 333.0 1 312.6 330.4 25.2
    50%以下
    Less than 50%    		 10 D/cm 9.9 12.7 11.5 0.9 7.5
    H/m 11.0 14.2 12.0 1.0 8.2
    林分密度/（株·hm?（br/>Stand density/(tree·ha?) 800.0 2 090.0 1 373.3 353.8 25.8
    下载: 导出CSV

    ?nbsp; 2天然兴安落叶松不同等级林木的样本统计野/p>

    Table 2.Sample statistics of different grades of naturalLarix gmelinii

    林木分级
    Tree classification    		 分组
    Group    		 样本?br/>Number of sample plot DBH/cm 树高 Tree height/m
    最小倻br/>Min. value 平均倻br/>Mean 最大倻br/>Max. value 最小倻br/>Min. value 平均倻br/>Mean 最大倻br/>Max. value
    优势 Dominant tree 建模数据 Modeling data 726 9.8 16.9 35.5 6.4 14.1 24.6
    检验数 Validation data 311 9.7 16.8 33.1 6.8 14.2 22.3
    平均 Average tree 建模数据 Modeling data 485 6.6 9.8 20.7 5.8 10.6 18.0
    检验数 Validation data 208 6.7 9.6 15.8 6.1 10.6 18.2
    被压 Pressed tree 建模数据 Modeling data 863 1.0 4.7 10.8 1.5 6.0 17.2
    检验数 Validation data 370 1.0 4.7 15.8 1.4 6.1 15.0
    下载: 导出CSV

    ?nbsp; 3候选立木树高−胸径曲线模型

    Table 3.Model of tree height-DBH curves for candidate standing trees

    序号 No. 模型 Model 表达 Expression
    1 Wykoff $ {{H}} = 1.3 + {{\rm{e}}^{\left( {{{a}} + \frac{{{b}}}{{{{D}} + 1}}} \right)}} $
    2 Richards ${{H}} = 1.3 + {{a}}{\left( {1 - {{\rm{e}}^{ - {{cD}}}}} \right)^{{b}}}$
    3 Weibull ${{H}} = 1.3 + {{a}}\left( {1 - {{\rm{e}}^{ - {{b}}{{{D}}^{{C}}}}}} \right) $
    4 Korf $ {{H}} = 1.3 + {{a}}{{\rm{e}}^{ - {{b}}{{{D}}^{-{{c}}}}}}$
    5 Logistic ${{H}} = 1.3 + {{a}}/\left( {1 + {{b}}{{\rm{e}}^{ - {{cD}}}}} \right)$
    注：a、b、c为模型参数。Notes:a,bandcare model parameters.
    下载: 导出CSV

    ?nbsp; 4天然兴安落叶松不同林木分级区间树高曲线模型的拟合

    Table 4.Fitting of tree height curve models for different tree grading intervals of naturalLarix gmelinii

    等级
    Grade    		 模型
    Model    		 参数 Parameter 拟合精度 Fitting accuracy
    a b c R2adj RMSE AIC
    优势?br/>Dominant tree Wykoff 3.203 4 ?1.432 4 0.486 1 2.020 4 1 024.201
    Richards 19.957 7 0.069 4 1.166 4 0.484 8 2.021 5 1 027.003
    Weibull 19.937 5 0.049 0 1.083 5 0.484 7 2.021 6 1 027.044
    Korf 26.811 2 7.568 0 0.829 5 0.485 6 2.020 0 1 025.915
    Logistic 18.276 9 3.632 2 0.128 5 0.482 7 2.025 7 1 030.001
    平均?br/>Average tree Wykoff 3.073 8 ?.161 6 0.379 8 1.707 9 522.206
    Richards 14.567 3 0.158 9 1.906 8 0.378 6 1.707 8 524.166
    Weibull 14.088 9 0.041 5 1.425 1 0.378 4 1.708 1 524.341
    Korf 18.948 2 8.673 7 1.094 8 0.379 0 1.707 3 523.881
    Logistic 13.450 8 6.193 4 0.267 3 0.378 0 1.708 7 524.673
    被压?br/>Pressed tree Wykoff 2.717 8 ?.431 7 0.761 2 1.232 1 363.302
    Richards 19.397 0 0.075 6 1.178 4 0.769 8 1.209 1 332.720
    Weibull 17.919 5 0.051 1 1.148 2 0.769 8 1.209 1 332.754
    Korf 8.406 0* 6.917 0 1.856 0 0.769 9 1.208 7 332.159
    Logistic 9.299 3 10.021 2 0.485 7 0.762 4 1.228 4 360.010
    注：*表示在显著性水平为0.05下渐迚i>t检验不显著。Notes:*indicates that the asymptotic for the parameter is not significant at the 0.05 level.
    下载: 导出CSV

    ?nbsp; 5不同参数组合哑变量树高−胸径模型拟合优度与评价指栆/p>

    Table 5.Goodness of fit and evaluation index of dummy variable model with different parameter combinations

    参数 Parameter R2adj RMSE AIC
    a 0.848 8 1.699 7 2 225.612
    a?i>b 0.858 8 1.642 4 2 081.902
    下载: 导出CSV

    ?nbsp; 6哑变量添加在a、b上的参数

    Table 6.Parameters of dummy variable added toaandb

    参数
    Parameter    		 a0 a1 a2 b0 b1 b2
    估计倻br/>Estimated value 2.689 9 0.490 5 0.410 3 ?.328 8 ?.772 9 ?.157 3
    下载: 导出CSV

    ?nbsp; 7分位数回归模型的参数估计

    Table 7.Parameter estimation of quantile regression model

    分位?br/>Quantile (τ) a b R2adj RMSE AIC
    0.1 2.906 7 ?0.193 5 0.615 4 2.673 3 4 123.071
    0.3 2.967 1 ?.020 3 0.810 0 1.905 2 2 703.786
    0.5 3.008 2 ?.401 5 0.849 8 1.693 8 2 211.037
    0.7 3.068 2 ?.982 1 0.814 9 1.880 5 2 649.209
    0.9 3.150 5 ?.373 0 0.583 3 2.821 1 4 348.549
    下载: 导出CSV

    ?nbsp; 8分位数回归模型的拟合与评件/p>

    Table 8.Fitting and evaluation of quantile regression model

    等级
    Grade    		 分位?br/>Quantile (τ)
    		 拟合精度 Fitting accuracy
    R2adj RMSE AIC
    优势?br/>Dominant tree 0.1 ?.448 8 3.392 4 1 776.681
    0.3 0.238 1 2.460 2 1 310.143
    0.5 0.430 0 2.127 8 1 099.402
    0.7 0.386 1 2.208 4 1 153.350
    0.9 ?.279 4 3.188 0 1 686.427
    平均?br/>Average tree 0.1 ?.624 8 2.764 4 989.327
    0.3 0.220 8 1.914 4 632.898
    0.5 0.377 5 1.711 1 524.047
    0.7 0.170 2 1.975 5 663.402
    0.9 ?.979 2 3.051 1 1 085.027
    被压?br/>Pressed tree 0.1 0.383 2 1.980 2 1 182.192
    0.3 0.687 9 1.408 5 594.248
    0.5 0.744 9 1.273 4 420.189
    0.7 0.668 9 1.450 8 645.321
    0.9 0.249 2 2.184 8 1 351.874
    注：粗体表示兴安落叶松林木等级模型统计量的最优值。下同。Notes: bold font indicates the optimal value of the model statistics ofLarix gmelinii. The same below.
    下载: 导出CSV

    ?nbsp; 9兴安落叶松不同方法的树高−胸径模型独立性检骋/p>

    Table 9.Validation statistics for tree height-DBH models ofLarix gmeliniibased on different methods

    等级
    Grade    		 模型
    Model    		 MAE MAPE
    优势?br/>Dominant tree 分位数模垊br/>Quantile regression 1.550 7 11.304 1
    哑变量模垊br/>Dummy variable model 1.522 9 11.258 4
    基础模型
    Basic model    		 1.561 4 11.400 5
    平均?br/>Average tree 分位数模垊br/>Quantile regression 1.461 8 13.778 2
    哑变量模垊br/>Dummy variable model 1.383 4 14.126 9
    基础模型
    Basic model    		 1.404 1 14.588 5
    被压?br/>Pressed tree 分位数模垊br/>Quantile regression 1.137 7 20.336 1
    哑变量模垊br/>Dummy variable model 0.800 2 13.578 2
    基础模型
    Basic model    		 0.907 9 16.265 0
    下载: 导出CSV
    • [2]赵俊? 亢新? 刘燕. 长白山主要针叶树种最优树高曲线研究[J]. 北京林业大学学报, 2009, 31(4): 13?8.doi:10.3321/j.issn:1000-1522.2009.04.003

    Zhao J H, Kang X G, Liu Y. Optimal height-diameter models for dominant coniferous species in Changbai Mountain, northeastern China[J]. Journal of Beijing Forestry University, 2009, 31(4): 13?8.doi:10.3321/j.issn:1000-1522.2009.04.003 [3]Luo R C, Lai C C. Multisensor fusion-based concurrent environment mapping and moving object detection for intelligent service robotics[J]. IEEE Transactions on Industrial Electronics, 2014, 61(8): 4043?051. [4]王冬? 张冬? 王方, ? 塞罕坝主要立地类型针阔混交林树高曲线构建[J]. 北京林业大学学报, 2016, 38(10): 7?4.doi:10.13332/j.1000-1522.20150359

    Wang D Z, Zhang D Y, Wang F, et al. Height curve construction of needle and broadleaved mixed forest under main site types in Saihanba, Hebei of northern China[J]. Journal of Beijing Forestry University, 2016, 38(10): 7?4.doi:10.13332/j.1000-1522.20150359 [5]王冬? 张冬? 张志? ? 基于非线性混合模型的针阔混交林树高与胸径关系[J]. 林业科学, 2016, 52(1): 30?6.

    Wang D Z, Zhang D Y, Zhang Z D, et al. Height-diameter relationship for conifer mixed forest based on nonlinear mixed-effects model[J]. Scientia Silvae Sinicae, 2016, 52(1): 30?6. [6]樊伟, 许崇? 崔珺, ? 基于混合效应的大别山地区杉木树高−胸径模型比较[J]. 应用生态学? 2017, 28(9): 2831?839.

    Fan W, Xu C H, Cui J, et al. Comparisons of height-diameter models of Chinese fir based on mixed effect in Dabie Mountain area, China[J]. Chinese Journal of Applied Ecology, 2017, 28(9): 2831?839. [7]曾翀, 雷相? 刘宪? ? 落叶松云冷杉林单木树高曲线的研究[J]. 林业科学研究, 2009, 22(2): 182?89.doi:10.3321/j.issn:1001-1498.2009.02.006

    Zeng C, Lei X D, Liu X Z, et al. Individual tree height-diameter curves of larch-spruce-fir forests[J]. Forest Research, 2009, 22(2): 182?89.doi:10.3321/j.issn:1001-1498.2009.02.006 [8]王君? 夏宛? 姜立? 基于分位数回归和哑变量模型的大兴安岭兴安落叶松树高−胸径模型[J]. 中南林业科技大学学报, 2020, 40(9): 24?2, 40.

    Wang J J, Xia W Q, Jiang L C. Height-diameter models forLarix gmeliniiin Daxing’anling based on quantile regression and dummy variable model[J]. Journal of Central South University of Forestry & Technology, 2020, 40(9): 24?2, 40. [9]张剑? 李彦? 张入匀, ? 基于枝条木材密度分级的鼎湖山南亚热带常绿阔叶林树高曲线模型[J]. 生物多样? 2021, 29(3): 456?66.doi:10.17520/biods.2020369

    Zhang J T, Li Y P, Zhang R Y, et al. Height-diameter models based on branch wood density classification for the south subtropical evergreen broad-leaved forest of Dinghushan[J]. Biodiversity Science, 2021, 29(3): 456?66.doi:10.17520/biods.2020369 [10]沈国? 翟明? 森林培育学[M]. 北京: 中国林业出版? 2011.

    Shen G F, Zhai M P. Silvicuture[M]. Beijing: China Forestry Publishing House, 2011. [11]Hegyi F. Growth models for tree and stand simulation[J]. Forestry Science, 1974, 26(3): 659?20. [12]Bohoras B, Cao Q V. Prediction of tree diameter growth using quantile regression and mixed-effects models[J]. Forest Ecology and Management, 2014, 319(5): 62?6. [13]Cao Q V, Wang J. Evaluation of methods for calibrating a tree taper equation[J]. Forest Science, 2015, 61(2): 213?19.doi:10.5849/forsci.14-008 [14]Özçelik R, Cao Q V, Trincado G, et al. Predicting tree height from tree diameter and dominant height using mixed-effects and quantile regression models for two species in Turkey[J]. Forest Ecology and Management, 2018, 419: 240?48. [15]Zang H, Lei X, Zeng W. Height-diameter equations for larch plantations in northern and northeastern China: a comparison of the mixed-effects, quantile regression and generalized additive models[J]. Forestry, 2016, 89(4): 434?45.doi:10.1093/forestry/cpw022 [16]高东? 邓华? 王海? ? 基于哑变量的蒙古栎林分生长模型[J]. 东北林业大学学报, 2014, 21(1): 61?4.doi:10.3969/j.issn.1000-5382.2014.01.014

    Gao D Q, Deng H F, Wang H B, et al. Dummy variables models inQuercus mongolicagrowth[J]. Journal of Northeast Forestry University, 2014, 21(1): 61?4.doi:10.3969/j.issn.1000-5382.2014.01.014 [17]孟宪? 测树学[M]. 北京: 中国林业出版? 2011: 125?160.

    Meng X Y. Forest measurement[M]. Beijing: China Forestry Publishing House, 2011: 125?160. [18]冯林, 王立? 林木生长分级数学表述的研究[J]. 内蒙古林学院学报, 1989, 11(1): 9?6.

    Feng L, Wang L M. Mathematical expression on crown classification[J]. Journal of Inner Mongolia Forestry University, 1989, 11(1): 9?6. [19]玉宝, 乌吉斯古? 王百? ? 大兴安岭兴安落叶?Larix gmelinii)天然林分级木转换特征[J]. 生态学? 2008, 28(11): 5750?757.doi:10.3321/j.issn:1000-0933.2008.11.062

    Yu B, Wujisiguleng, Wang B T, et al. Analysis on classified stem transformation characteristic ofLarix gmeliniinatural forest at Daxing’anling Mountains[J]. Acta Ecologica Sinica, 2008, 28(11): 5750?757.doi:10.3321/j.issn:1000-0933.2008.11.062 [20]康永? 罗宁, 欧建? 造林密度对南方红豆杉人工林生长性状的影响[J]. 西南林业大学学报(自然科学), 2017, 37(3): 47?2.

    Kang Y W, Luo N, Ou J D. Effects of planting density on the growth traits ofTaxus wallichinaplantation[J]. Journal of Southwest Forestry University (Natural Science Edition), 2017, 37(3): 47?2. [21]欧建? 吴志? 峦大杉人工林树冠、根系生长和林木分级的早期密度效应[J]. 东北林业大学学报, 2018, 46(12): 15?9.doi:10.3969/j.issn.1000-5382.2018.12.003

    Ou J D, Wu Z Z. Early density effect growth of grown and root, and forest classification ofCunninghamia konishiiplantation[J]. Journal of Northeast Forestry University, 2018, 46(12): 15?9.doi:10.3969/j.issn.1000-5382.2018.12.003 [22]李海? 法蕾. 基于分级的全国主要树种树高−胸径模型[J]. 林业科学, 2011, 47(10): 83?0.doi:10.11707/j.1001-7488.20111013

    Li H K, Fa L. Height-diameter model for major tree species in China using the classified height method[J]. Scientia Silvae Sinicae, 2011, 47(10): 83?0.doi:10.11707/j.1001-7488.20111013 [23]段光? 李学? 冯岩, ? 华北落叶松天然次生林树高曲线的混合效应模型[J]. 南京林业大学学报(自然科学?, 2018, 42(2): 163?69.

    Duan G S, Li X D, Feng Y, et al. Developing a height-diameter relationship model with mixed random effects forLarix principis-rupprechtiinatural secondary forests[J]. Journal of Nanjing Forestry University (Natural Science Edition), 2018, 42(2): 163?69. [24]朱光? 胡松, 符利? 基于哑变量的湖南栎类天然林林分断面积生长模型[J]. 南京林业大学学报(自然科学?, 2018, 42(2): 157?62.

    Zhu G Y, Hu S, Fu L Y. Basal area growth model for oak natural forest in Hunan Province based on dummy variable[J]. Journal of Nanjing Forestry University (Natural Science Edition), 2018, 42(2): 157?62. [25]曹梦, 潘萍, 欧阳勋志, ? 基于哑变量的闽楠天然次生林单木胸径和树高生长模型研究[J]. 北京林业大学学报, 2019, 41(5): 88?6.doi:10.13332/j.1000-1522.20190026

    Cao M, Pan P, Ouyang X Z, et al. Growth model of DBH and tree height for individual tree of natural secondaryPhoebe bourneiforest based on dummy variable[J]. Journal of Beijing Forestry University, 2019, 41(5): 88?6.doi:10.13332/j.1000-1522.20190026 [26]臧颢, 雷相? 张会? ? 红松树高−胸径的非线性混合效应模型研究[J]. 北京林业大学学报, 2016, 38(6): 8?.

    Zang H, Lei X D, Zhang H R, et al. Nonlinear mixed-effects height-diameter model ofPinus koraiensis[J]. Journal of Beijing Forestry University, 2016, 38(6): 8?. [27]吕飞? 基于CSI的蒙古栎林木竞争与分级研究[D]. 长沙: 中南林业科技大学, 2016.

    Lü F Z. Study on the forest competition and classification ofQuercus mongolicabased onCIS[D]. Changsha: Central South University of Forestry and Technology, 2016. [28]张冬? 王冬? 李晓, ? 基于分位数回归的针阔混交林树高与胸径的关系[J]. 浙江农林大学学报, 2020, 37(3): 424?31.doi:10.11833/j.issn.2095-0756.20190461

    Zhang D Y, Wang D Z, Li X, et al. Relationship between height and diameter at breast height (DBH) in mixed coniferous and broadleaved forest based on quantile regression[J]. Journal of Zhejiang A&F University, 2020, 37(3): 424?31.doi:10.11833/j.issn.2095-0756.20190461 [29]李杰. 基于分级的福建将乐地区栲树树高曲线模型研究[J]. 西北农林科技大学学报(自然科学?, 2019, 47(11): 34?2.doi:10.13207/j.cnki.jnwafu.2019.11.005

    Li J. Classification based height-diameter model forCastanopsis fargesiiin Jiangle, Fujian[J]. Journal of Northwest A&F University (Natural Science Edition), 2019, 47(11): 34?2.doi:10.13207/j.cnki.jnwafu.2019.11.005 [30]雷相? 李希? 混交林生长模型研究进展[J]. 北京林业大学学报, 2003, 25(3): 105?10.doi:10.3321/j.issn:1000-1522.2003.03.022

    Lei X D, Li X F. A review on growth models of mixed forests[J]. Journal of Beijing Forestry University, 2003, 25(3): 105?10.doi:10.3321/j.issn:1000-1522.2003.03.022
    相关文章
  • 施引文献
  • 资源附件 (0)
  • 加载? /> <div class=
    WeChat 点击查看大图
    ?3)/ ?9)
    计量
    • 文章访问?93
    • HTML全文浏览野14
    • PDF下载野41
    • 被引次数:0
    出版历程
    • 收稿日期:2021-05-13
    • 修回日期:2023-03-25
    • 录用日期:2023-03-30
    • 网络出版日期:2023-04-01

    目录

      返回
          Baidu
          map