高级检索

留言板

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题, 您可以本页添加留言。我们将尽快给您答复。谢谢您的支持!

姓名
邮箱
手机号码
标题
留言内容
验证码

基于气候因子的兴安落叶松天然林单木直径生长模型

杨鑫 王建军 杜志 王文文 孟京辉

杨鑫, 王建军, 杜志, 王文文, 孟京辉. 基于气候因子的兴安落叶松天然林单木直径生长模型[J]. 北京林业大学学报. doi: 10.12171/j.1000-1522.20210353
引用本文: 杨鑫, 王建军, 杜志, 王文文, 孟京辉. 基于气候因子的兴安落叶松天然林单木直径生长模型[J]. 北京林业大学学报. doi: 10.12171/j.1000-1522.20210353
Yang Xin, Wang Jianjun, Du Zhi, Wang Wenwen, Meng Jinghui. Individual-tree diameter increment model for natural Larix gmelinii forests based on climatic factors[J]. Journal of Beijing Forestry University. doi: 10.12171/j.1000-1522.20210353
Citation: Yang Xin, Wang Jianjun, Du Zhi, Wang Wenwen, Meng Jinghui. Individual-tree diameter increment model for natural Larix gmelinii forests based on climatic factors[J]. Journal of Beijing Forestry University. doi: 10.12171/j.1000-1522.20210353

基于气候因子的兴安落叶松天然林单木直径生长模型

doi: 10.12171/j.1000-1522.20210353
基金项目: 国家林业和草原局重点工程项目前期研究项目(500102-5103),内蒙森工集团科技支撑项目(NXLKJ﹝2021﹞005-1)
详细信息
    作者简介:

    杨鑫。主要研究方向:森林生长收获与模型模拟。Email:yang_xin1201@163.com 地址:100083 北京市海淀区清华东路35号北京林业大学林学院

    责任作者:

    孟京辉,博士,副教授。主要研究方向:森林经营与管理。Email:Jmeng@bjfu.edu.cn 地址:同上

  • 中图分类号: S791.22

Individual-tree diameter increment model for natural Larix gmelinii forests based on climatic factors

  • 摘要:   目的  建立基于气候因子的兴安落叶松天然林单木直径生长模型用于预测胸径生长,为内蒙古大兴安岭地区兴安落叶松天然林经营管理提供理论依据。  方法  基于内蒙古大兴安岭地区2013、2018年森林资源连续清查数据中的187块兴安落叶松天然林固定样地及样地位置对应的气候数据,运用逐步回归法建立考虑气候因子的传统单木直径生长模型,并在此基础上,加入样地效应构建兴安落叶松单木直径生长混合效应模型。最后,利用独立检验样本数据对基础模型和混合效应模型进行检验。  结果  年平均气温MAT、生长季平均降雨量Pgm是影响该地区兴安落叶松胸径生长量的主要气候因素,二者与胸径生长量均呈正相关。其余显著影响胸径生长量的因子包括初期胸径的倒数(1/DBH)、大于对象木的断面积和(BAL)、每公顷株数(NT),3个变量都与胸径生长量呈负相关。胸径混合效应模型的决定系数(R2)、平均绝对误差(MAE)和均方根误差(RMSE)分别为0.760 4,0.386 6和0.486 3 cm。与基础模型相比,混合效应模型的R2提高了0.321 7,MAE和RMSE减少了0.230 6和0.267 4 cm。在模型检验中,混合效应模型也呈现出了较好的拟合效果。  结论  基于气候因子的单木直径生长混合效应模型可以较好地描述内蒙古大兴安岭地区的兴安落叶松胸径生长过程。

     

  • 图  1  基础模型的残差图和QQ图

    Figure  1.  Residual plot and QQ plot of the basic model

    图  2  混合效应模型的残差图和QQ图

    Figure  2.  Residual plot and QQ plot of the mixed-effects model

    图  3  基础模型和混合效应模型的观测值和拟合值的关系

    Figure  3.  Relationship between observed values and fitted values of basic model and mixed-effects model

    表  1  兴安落叶松天然林样地及样木数据

    Table  1.   Sample plots and sample trees data information for natural Larix gmelinii forests

    变量 Variable变量符号 Variable symbol最小值 Min.最大值 Max.均值 Mean标准差 SD
    初期胸径 Initial DBH/cm DBH 5.0 53.1 12.1 6.5
    胸径生长量 DBH increment/cm iDBH 0.1 5.4 0.7 0.6
    样地平均胸径 Quadratic mean diameter/cm QMD 7.0 31.9 13.9 4.3
    每公顷株数/(株·hm−2) the number of trees/(trees·ha−1) NT 75 3 060 929 542
    每公顷断面积/(m2·hm−2) Basal area per hectare/(m2·ha−1) BAS 0.48 34.05 12.65 6.64
    海拔 Elevation/m EL 386 1 655 885 204
    坡度 Slope degree/(°) SL 0.0 29.0 6.4 5.7
    坡向 Aspect/(°) ASP 0.0 315.0 145.0 106.8
    土层厚度 Soil depth/cm ST 3 65 26 12
    注:坡向(ASP)按照逆时针方向依次规定:正北0°、正西90°、正南180°、正东270°。Note: The aspect according to the anticlockwise direction and provides: The north is 0°, west is 90°, south is 180°, east is 270°.
    下载: 导出CSV

    表  2  2013—2018年期间兴安落叶松天然林样地气候变量统计

    Table  2.   Climatic variable statistics of the sample plots for natural Larix gmelinii forests in 2013—2018

    变量
    Variable
    变量符号
    Variable symbol
    最小值
    Min.
    最大值
    Max.
    平均值
    Mean
    标准差
    SD
    年平均气温
    Mean annual temperature/℃
    MAT −4.00 0.02 −2.60 0.74
    最热月温度
    Mean warmest month temperature/℃
    MWMT 16.14 20.10 18.13 0.70
    最冷月气温
    Mean coolest month temperature/℃
    MCMT −28.06 −22.12 26.18 0.97
    生长季最低气温
    Minimum temperature of growing season/℃
    Tgmin 3.58 8.41 5.79 0.92
    生长季最高气温
    Maximum temperature of growing season/℃
    Tgmax 18.14 22.38 20.50 0.69
    生长季平均气温
    Mean temperature of growing season/℃
    Tgm 10.86 15.30 13.14 0.78
    年平均降雨量
    Mean annual precipitation/mm
    MAP 414.40 535.80 466.13 26.26
    生长季平均降雨量
    Mean precipitation of growing season/mm
    Pgm 70.32 93.28 80.20 4.54
    下载: 导出CSV

    表  3  兴安落叶松单木直径生长模型参数估计结果

    Table  3.   Results of parameter estimation of Larix gmelinii individual-tree diameter growth model

    自变量
    Variable
    系数 Coefficient标准差
    SD
    tP方差膨胀因子 VIF
    Intercept 3.599 0 0.204 0 17.645 < 0.000 1
    $ \dfrac{1}{\mathrm{D}\mathrm{B}\mathrm{H}} $ −10.570 0 0.235 2 −44.951 < 0.000 1 1.110 9
    BAL −0.666 4 0.028 1 −23.682 < 0.000 1 1.216 9
    NT −0.000 2 0.000 0 −10.913 < 0.000 1 1.141 0
    MAT 0.253 7 0.014 6 17.378 < 0.000 1 1.049 4
    Pgm 0.017 0 0.002 4 7.072 < 0.000 1 1.044 4
    下载: 导出CSV

    表  4  不同随机参数组合的混合效应模型部分结果

    Table  4.   Partial results of combinations of different random parameters for mixed-effects model

    模型 Model随机参数 Random parametersAICBICLoglikLRTP
    基础模型 Basic Model 无 None 12 909.2 12 955.7 −6 447.6
    模拟1 Model 1 Int 9 784.8 9 837.9 −4 884.4
    模拟2 Model 2 Int、1/DBH 9 104.6 9 171.1 −4 542.3 684.15 < 0.000 1
    模拟3 Model 3 Int、1/DBH、BAL 9 047.5 9 133.9 −4 510.8 63.08 < 0.000 1
    模拟4 Model 4 1/DBH、BAL、NT、MAT 9 041.7 9 154.6 −4 503.8 13.88 0.007 7
    模拟5 Model 5 Int、1/DBH、BAL、NT、MAT 9 038.8 9 185.0 −4 497.4 12.84 0.024 9
    模拟6 Model 6 Int、1/DBH、BAL、NT、MAT、Pgm 9 050.7 9 236.7 −4 497.3 0.16 0.999 9
    注:AIC为赤池信息准则,即Akaike information criterion;BIC为贝叶斯信息准则,即Bayesian Information Criterions;Loglik为对数似然值,即Log-Likelihood;LRT为似然比检验值,即Likelihood ratio test。Note: AIC is Akaike information criterion; BIC is Bayesian Information Criterions; Loglik is Log-Likelihood; LRT is Likelihood ratio test.
    下载: 导出CSV

    表  5  3种随机参数协方差结构混合效应模型对比

    Table  5.   Comparison of mixed-effects models with three covariance structures of random parameter

    矩阵 StructuresAICBICLoglikLRTP
    广义正定矩阵 General positive-definite matrix 9 038.8 9 185.0 −4 497.4
    复合对称 Compound symmetry 9 910.5 9 970.3 −4 946.3 897.70 < 0.000 1
    对角矩阵 Diagonal matrix 9 187.7 9 267.4 −4 581.9 168.88 < 0.000 1
    下载: 导出CSV

    表  6  考虑异方差和自相关后混合效应模型对比

    Table  6.   Comparison of mixed-effects model considering variance functions and autocorrelation structures

    模型
    Model
    异方差函数
    Variance Function
    自相关结构
    Correlation Structure
    AICBICLoglikLRTP
    (1) 无 None 无 None 9 038.8 9 185.0 −4 497.4
    (2) 常数加幂函数 ConstPower 无 None 9 025.3 9 184.7 −4 488.6 17.56 0.000 2
    (3) 幂函数 Power 无 None 9 025.4 9 178.2 −4 489.7 15.40 0.000 1
    (4) 指数函数 Exponent 无 None 9 003.8 9 156.6 −4 478.9 37.00 < 0.000 1
    (5) 指数函数 Exponent 复合对称 CS 9 001.6 9 161.0 −4 476.8 4.26 0.039 1
    (6) 指数函数 Exponent 一阶自回归结构 AR(1) 8 833.4 8 992.9 −4 392.7 172.42 < 0.000 1
    (7) 指数函数 Exponent 一阶自回归移动平均结构 ARMA(1, 1) 不收敛 Non convergence
    下载: 导出CSV

    表  7  兴安落叶松单木胸径生长模型建模结果对比

    Table  7.   Modeling results comparison of individual-tree DBH growth models for Larix gmelinii

    模型 ModelAICBICR2MAERMSE
    基础模型
    Basic model
    12 909.2 12 955.7 0.438 7 0.617 2 0.753 7
    混合效应模型
    Mixed-effects model
    8 833.4 8 992.9 0.760 4 0.386 6 0.486 3
    下载: 导出CSV

    表  8  兴安落叶松单木胸径生长模型检验结果对比

    Table  8.   Validation results comparison of individual-tree DBH growth models for Larix gmelinii

    模型 ModelR2MAERMSE
    基础模型 Basic model 0.472 9 0.601 6 0.740 9
    混合效应模型 Mixed-effects model 0.765 6 0.393 0 0.494 1
    下载: 导出CSV
  • [1] 张海平, 李凤日, 董利虎, 等. 基于气象因子的白桦天然林单木直径生长模型[J]. 应用生态学报, 2017, 28(6): 1851−1859. doi: 10.13287/j.1001-9332.201706.009

    Zhang H P, Li F R, Dong L H, et al. Individual tree diameter increment model for natural Betula platyphylla forests based on meteorological factors[J]. Chinese Journal of Applied Ecology, 2017, 28(6): 1851−1859. doi: 10.13287/j.1001-9332.201706.009
    [2] 杜志, 陈振雄, 孟京辉, 等. 基于混合效应的马尾松单木断面积预估模型[J]. 中南林业科技大学学报, 2020, 40(9): 33−40.

    Du Z, Chen Z X, Meng J H, et al. Prediction model of individual-tree basal area for Pinus massoniana based on mixed effect[J]. Journal of Central South University of Forestry & Technology, 2020, 40(9): 33−40.
    [3] 李春明. 基于两层次线性混合效应模型的杉木林单木胸径生长量模型[J]. 林业科学, 2012, 48(3): 66−73. doi: 10.11707/j.1001-7488.20120311

    Li C M. Individual tree diameter increment model for Chinese fir plantation based on two-level linear mixed effects models[J]. Scientia Silvae Sinicae, 2012, 48(3): 66−73. doi: 10.11707/j.1001-7488.20120311
    [4] 杜纪山. 用二类调查样地建立落叶松单木直径生长模型[J]. 林业科学研究, 1999, 12(2): 160−164. doi: 10.3321/j.issn:1001-1498.1999.02.008

    Du J S. Modeling individual tree growth of Larix by using forest management inventory plots[J]. Forest Research, 1999, 12(2): 160−164. doi: 10.3321/j.issn:1001-1498.1999.02.008
    [5] 刘平, 马履一, 王玉涛, 等. 油松中幼龄人工林单木胸径生长模型研究[J]. 沈阳农业大学学报, 2009, 40(2): 197−201. doi: 10.3969/j.issn.1000-1700.2009.02.016

    Liu P, Ma L Y, Wang Y T, et al. Individual DBH growth model of Pinus tabulaeformis young-middle aged plantation[J]. Journal of Shenyang Agricultural University, 2009, 40(2): 197−201. doi: 10.3969/j.issn.1000-1700.2009.02.016
    [6] 马武, 雷相东, 徐光, 等. 蒙古栎天然林单木生长模型研究−Ⅰ. 直径生长量模型[J]. 西北农林科技大学(自然科学版), 2015, 43(2): 99−105.

    Ma W, Lei X D, Xu G, et al. Growth models for natural Quercus mongolica forests −Ⅰ. diameter growth model[J]. Journal of Northwest A & F University (Natural Science Edition), 2015, 43(2): 99−105.
    [7] 闫明准, 刘兆刚. 帽儿山地区次生林椴树单木胸高断面积生长模型的研究[J]. 森林工程, 2009, 25(2): 1−4,21. doi: 10.3969/j.issn.1001-005X.2009.02.001

    Yan M Z, Liu Z G. Study on growth model of section area of breast height of Tilia amurensis individual tree of secondary forest in Mao’ershan Mountain region[J]. Forest Engineering, 2009, 25(2): 1−4,21. doi: 10.3969/j.issn.1001-005X.2009.02.001
    [8] 卢军. 长白山地区天然混交林单木生长模型的研究[D]. 哈尔滨: 东北林业大学, 2005.

    Lu J. Individual tree growth models for natural mixed forests in the region of Changbai Mountains[D]. Harbin: Northeast Forestry University, 2005.
    [9] 王建军, 曾伟生, 孟京辉. 考虑预估期间林木枯死及采伐影响的杉木单木胸高断面积生长模型研究[J]. 西北林学院学报, 2017, 32(3): 181−185. doi: 10.3969/j.issn.1001-7461.2017.03.34

    Wang J J, Zeng W S, Meng J H. Individual-tree basal area growth model for Cunninghamia lanceolata with the consideration of thinning and tree mortality in the prediction interval[J]. Journal of Northwest Forestry University, 2017, 32(3): 181−185. doi: 10.3969/j.issn.1001-7461.2017.03.34
    [10] 臧颢. 区域尺度气候敏感的落叶松人工林林分生长模型[D]. 北京: 中国林业科学研究院, 2016.

    Zang H. Regional-scale climate-sensitive stand growth models for larch plantations[D]. Beijing: Chinese Academy of Forestry, 2016.
    [11] 桑杰. 基于R语言的气候影响下青冈栎非线性混合效应生长预测模型[D]. 长沙: 中南林业科技大学, 2019.

    Sang J. Nonlinear mixed effect growth prediction model of Quercus glauca under climatic influence based on R language[D]. Changsha: Central South University of Forestry & Technology, 2019.
    [12] Subedi N, Sharma M. Climate-diameter growth relation-ships of black spruce and jack pine trees in boreal Ontario, Canada[J]. Global Change Biology, 2013, 19: 506−516.
    [13] Subedi N, Sharma M. Individual-tree diameter growth models for black spruce and jack pine plantations in northern Ontario[J]. Forest Ecology and Management, 2011, 261(11): 2140−2148. doi: 10.1016/j.foreco.2011.03.010
    [14] 刘帅, 李建军, 卿东升, 等. 气候敏感的青冈栎单木胸径生长模型[J]. 林业科学, 2021, 57(1): 95−104. doi: 10.11707/j.1001-7488.20210110

    Liu S, Li J J, Qing D S, et al. A climatic-sensitive individual-tree DBH growth model for Cyclobalanopsis glauca[J]. Scientia Silvae Sinicae, 2021, 57(1): 95−104. doi: 10.11707/j.1001-7488.20210110
    [15] 齐战涛, 朱光玉, 许冰冰, 等. 含气候效应的湖南杉木人工林断面积生长模型[J]. 中南林业科技大学学报, 2021, 41(5): 66−73.

    Qi Z T, Zhu G Y, Xu B B, et al. Basal area growth model of Cunninghamia lanceolata plantation in Hunan province with climate effect[J]. Journal of Central South University of Forestry & Technology, 2021, 41(5): 66−73.
    [16] Wang M, Zhao Y H, Zhen Z, et al. Individual-tree diameter growth model for Korean pine plantations based on optimized interpolation of meteorological variables[J]. Journal of Forestry Research, 2021, 32(4): 1535−1552. doi: 10.1007/s11676-020-01177-9
    [17] 余黎, 雷相东, 王雅志, 等. 基于广义可加模型的气候对单木胸径生长的影响研究[J]. 北京林业大学学报, 2014, 36(5): 22−32.

    Yu L, Lei X D, Wang Y Z, et al. Impact of climate on individual tree radial growth based on generalized additive model[J]. Journal of Beijing Forestry University, 2014, 36(5): 22−32.
    [18] 欧强新, 雷相东, 沈琛琛, 等. 基于随机森林算法的落叶松-云冷杉混交林单木胸径生长预测[J]. 北京林业大学学报, 2019, 41(9): 9−19.

    Ou X Q, Lei X D, Shen C C, et al. Individual tree DBH growth prediction of larch-spruce-fir mixed forests based on random forest algorithm[J]. Journal of Beijing Forestry University, 2019, 41(9): 9−19.
    [19] 王震, 鲁乐乐, 张雄清, 等. 基于贝叶斯模型平均法构建杉木林分蓄积量生长模型[J]. 林业科学研究, 2021, 34(3): 64−71.

    Wang Z, Lu L L, Zhang X Q, et al. Stand volume growth model Chinese fir plantations based on bayesian model averaging approach[J]. Forest Research, 2021, 34(3): 64−71.
    [20] Saud P, Lynch T B, Cram D S, et al. An annual basal area growth model with multiplicative climate modifier fitted to longitudinal data for short leaf pine[J]. Forestry, 2019, 5: 1−16.
    [21] Jordan L, Daniels R F, Clark A III, et al. Multilevel nonlinear mixed-effects models for the modeling of earlywood and latewood microfibril angle[J]. Forest Science, 2005, 51(4): 357−371.
    [22] 彭娓, 李凤日, 董利虎. 黑龙江省长白落叶松人工林单木生长模型[J]. 南京林业大学学报(自然科学版), 2018, 42(3): 19−27.

    Peng W, Li F R, Dong L H, et al. Individual tree diameter growth model for Larix olgensis plantation in Heilongjiang Province, China[J]. Journal of Nanjing Forestry University (Natural Sciences Edition), 2018, 42(3): 19−27.
    [23] 许昊, 孙玉军, 王新杰, 等. 利用线性混合效应模型模拟杉木人工林枝条生物量[J]. 应用生态学报, 2015, 26(10): 2969−2977.

    Xu H, Sun Y J, Wang X J, et al. Simulation of the branch biomass for Chinese fir plantation using the linear mixed effects model[J]. Chinese Journal of Applied Ecology, 2015, 26(10): 2969−2977.
    [24] 邱思玉, 孙玉军. 长白落叶松人工林单木冠幅模型[J]. 东北林业大学学报, 2021, 49(2): 49−53.

    Qiu S Y, Sun Y J. Individual tree crown width prediction models for Larix olgensis plantation[J]. Journal of Northeast Forestry University, 2021, 49(2): 49−53.
    [25] 王帅玲, 龙时胜, 曾思齐, 等. 湖南栎类次生林林分断面积生长模型[J]. 中南林业科技大学学报, 2021, 41(8): 84−91.

    Wang S L, Long S S, Zeng S Q, et al. Basal area growth model of oak secondary forest in Hunan province[J]. Journal of Central South University of Forestry & Technology, 2021, 41(8): 84−91.
    [26] 王少杰, 邓华锋, 向玮, 等. 基于混合模型的油松林分蓄积量预测模型的建立[J]. 西北农林科技大学学报(自然科学版), 2018, 46(2): 29−38, 46.

    Wang S J, Deng H F, Xiang W, et al. Establishment of predicting models for Pinus tabulaeformis stands volume based on mixed models[J]. Journal of Northwest A & F University (Natural Science Edition), 2018, 46(2): 29−38, 46.
    [27] 蒋延玲. 全球变化的中国北方林生态系统生产力及其生态系统公益[D]. 北京: 中国科学院植物研究所, 2001.

    Jiang Y L. Study on the productivity of Chinese boreal forest ecosystem under global change and ecosystem service assessment[D]. Beijing: Institute of Botany, the Chinese Academy of Sciences, 2001.
    [28] 陆玉宝. 兴安落叶松天然林林分结构与生产力特征的研究[D]. 呼和浩特: 内蒙古农业大学, 2006.

    Lu Y B. Study on the characteristics of stand structure and productivity in Larix gmelinii natural forest[D]. Hohhot: Inner Mongolia Agricultural University, 2006.
    [29] 高旭. 内蒙古大兴安岭重点国有林区经济转型发展研究[D]. 通辽: 内蒙古民族大学, 2017.

    Gao X. Study on economic transition and development of key stated-owned forest areas in Daxing’an mountains of Inner Mongolia[D]. Tongliao: Inner Mongolia University For Nationalities, 2017.
    [30] 萨如拉, 王雪鑫, 徐加睿, 等. 大兴安岭兴安落叶松天然林单木生长规律与模型研究[J]. 西南林业大学学报(自然科学), 2020, 40(2): 111−116.

    Sa R L, Wang X X, Xu J R, et al. Study on the growth and models of single tree of Larix gmelinii natural forest in Daxing’an mountains[J]. Journal of southwest forestry university (Natural Sciences), 2020, 40(2): 111−116.
    [31] Wang T, Hamann A, Spittlehouse D L, et al. Climatewna-high-resolution spatial climate data for western north America[J]. Journal of Applied Meteorology and Climatology, 2012, 51(1): 16−29. doi: 10.1175/JAMC-D-11-043.1
    [32] 刘浩, 张秋良. 兴安落叶松林生长季蒸散量特征[J]. 中南林业科技大学学报, 2021, 41(3): 149−156.

    Liu H, Zhang Q L. Characteristics of evapotranspiration in Larix gmelinii forest during growing seasons[J]. Journal of Central South University of Forestry & Technology, 2021, 41(3): 149−156.
    [33] Bella I E. A new competition model for individual trees[J]. Forest Science, 1971, 17: 364−372.
    [34] Wykoff W R. A basal area increment model for individual conifer in the northern Rocky Mountains[J]. Forestry Science, 1990, 36: 1077−1104.
    [35] 王蒙, 李凤日. 基于抚育间伐效应的长白落叶松人工林单木直径生长模型[J]. 南京林业大学学报(自然科学版), 2018, 42(3): 28−36.

    Wang M, Li F R. Modelling individual tree diameter growth for Larix olgensis based on thinning effects[J]. Journal of Nanjing Forestry University (Natural Sciences Edition), 2018, 42(3): 28−36.
    [36] 陈国栋, 杜研, 丁佩燕, 等. 基于混合效应模型的新疆天山云杉单木胸径预测模型构建[J]. 北京林业大学学报, 2020, 42(7): 12−22. doi: 10.12171/j.1000-1522.20190236

    Chen G D, Du Y, Ding P Y, et al. Predicting model construction of single tree DBH of Picea schrenkiana in Xinjiang of northwestern China based on mixed effects model[J]. Journal of Beijing Forestry University, 2020, 42(7): 12−22. doi: 10.12171/j.1000-1522.20190236
    [37] Wang Y, Lemay V M, Baker T G. Modelling and prediction of dominant height and site index of Eucalyptus globules plantations using a nonlinear mixed-effects model approach[J]. Canadian Journal of Forest Research, 2007, 37(8): 1390−1403. doi: 10.1139/X06-282
    [38] Vonesh E F , Chinchilli V M . Linear and nonlinear models for the analysis of repeated measurements[M]. New York: Marcel Dekker Inc, 1997.
    [39] Monserud R A, Yang Y, Huang S, et al. Potential change in lodgepole pine site index and distribution under climatic change in Alberta[J]. Canadian Journal of Forest Research, 2008, 38(2): 343−352. doi: 10.1139/X07-166
    [40] Huang J G, Yves B, Frank B, et al. Impact of future climate on radial growth of four major boreal tree species in the eastern Canadian boreal forest[J/OL]. PLoS One, 2013, 8(2): e56758[2013−2−28]. https://doi.org/10.1371/journal.pone.0056758.
    [41] 白学平, 常永兴, 张先亮, 等. 近30年快速升温对两种典型小地形上兴安落叶松径向生长的影响[J]. 应用生态学报, 2016, 27(12): 3853−3861.

    Bai X P, Chang Y X, Zhang X L, et al. Impacts of rapid growth of Larix gmelinii on two typical micro-topographies in the recent 30 years[J]. Chinese Journal of Applied Ecology, 2016, 27(12): 3853−3861.
    [42] 张朋磊, 刘滨辉. 气候变化对不同纬度兴安落叶松径向生长的影响[J]. 东北林业大学学报, 2015, 43(3): 10−13,22. doi: 10.3969/j.issn.1000-5382.2015.03.003

    Zhang P L, Liu B H. Effect of climate change on Larix gmelinii growth in different latitudes[J]. Journal of Northeast Forestry University, 2015, 43(3): 10−13,22. doi: 10.3969/j.issn.1000-5382.2015.03.003
    [43] Liang E Y, Shao X M, Hu Y X, et al. Dendroclimatic evaluation of climate-growth relationships of Meyer spruce (Picea meyeri) on a sandy substrate in semi-arid grassland, north China[J]. Trees, 2001, 15(4): 230−235. doi: 10.1007/s004680100097
    [44] Deslauriers A, Huang J G, Balducci L, et al. The contribution of carbon and water in modulating wood formation in black spruce saplings[J]. Plant Physiology, 2016, 170(4): 2072−2084. doi: 10.1104/pp.15.01525
    [45] Huang S, Titus S J. An individual tree diameter increment model for white spruce in Alberta[J]. Revue Canadienne De Recherche Forestière, 1995, 25(9): 1455−1465.
    [46] Adame P, Hynynen J, Cañellas I, et al. Individual-tree diameter growth model for rebollo oak (Quercus pyrenaica Willd.) coppices[J]. Forest Ecology and Management, 2008, 255(3-4): 1011−1022. doi: 10.1016/j.foreco.2007.10.019
    [47] Zhang X. A linkage among whole-stand model, individual-tree model and diameter-distribution model[J]. Journal of Forest Science, 2010, 56(56): 600−608.
    [48] Yang Y, Titus S J & Huang S. Modeling individual tree mortality for white spruce in Alberta[J]. Ecological Modelling, 2003, 163(3): 209−222. doi: 10.1016/S0304-3800(03)00008-5
    [49] Condés S, Sterba H. Comparing an individual tree growth model for Pinus halepensis Mill. in the Spanish region of Murcia with yield tables gained from the same area[J]. European Journal of Forest Research, 2008, 127(3): 253−261. doi: 10.1007/s10342-007-0201-7
    [50] Kim M, Lee W K, Kim Y S, et al. Impact of thinning intensity on the diameter and height growth of Larix kaempferi stands in central Korea[J]. Forest Science and Technology, 12(2): 77-87.
    [51] Graham J S. Thinning increases diameter growth of paper Birch in the Susitna Valley, Alaska: 20 year results[J]. Northern Journal of Applied Forestry, 1998, 15(3): 113−115. doi: 10.1093/njaf/15.3.113
    [52] Rytter L. Effects of thinning on the obtainable biomass, stand density, and tree diameters of intensively grown grey alder plantations[J]. Forest Ecology and Management, 1995, 73(1-3): 135−143. doi: 10.1016/0378-1127(94)03498-L
    [53] Uzoh F C C, Oliver W W. Individual tree height increment model for managed even-aged stands of ponderosa pine throughout the western United States using linear mixed effects models[J]. Forest Ecology and Management, 2006, 221(1-3): 147−154. doi: 10.1016/j.foreco.2005.09.012
    [54] Calama R, Montero G. Multilevel linear mixed model for tree diameter increment in stone pine (Pinus pinea): a calibrating approach[J]. Silva Fennica, 2005, 39: 37−54.
    [55] 符利勇, 唐守正, 张会儒, 等. 基于多水平非线性混合效应蒙古栎林单木断面积模型[J]. 林业科学研究, 2015, 28(1): 23−31.

    Fu L Y, Tang S Z, Zhang H R, et al. Multilevel nonlinear mixed-effects basal area models for individual trees of Quercus mongolica[J]. Forest Research, 2015, 28(1): 23−31.
  • 加载中
图(3) / 表(8)
计量
  • 文章访问数:  56
  • HTML全文浏览量:  7
  • PDF下载量:  23
  • 被引次数: 0
出版历程
  • 收稿日期:  2021-09-07
  • 修回日期:  2022-03-03
  • 网络出版日期:  2022-08-03

目录

    /

    返回文章
    返回