Estimating DBH of Cunninghamia lanceolata based on crown and competition factors
-
摘要:
目的 无人机遥感的迅速发展为胸径预估提供了新方向，本研究适用于通过无人机遥感技术提取样地单木树冠因子后，估算胸径及林分每公顷断面积等指标，实现精准高效的森林资源监测与管理。 方法 根据福建省将乐国有林场33块杉木人工林地面调查数据，利用10种传统模型与2种机器学习方法分别对单木胸径进行估测，并基于不同的自变量组合形式来分析不同因子对胸径估测的影响。 结果 根据传统模型参数拟合结果可以看出，树冠半径与胸径呈显著正相关，林分密度、偏冠因子及竞争指数与胸径均呈显著负相关。传统模型建模过程中所引入最优竞争指数为树冠重叠内角相关的CI2，模型逻辑斯蒂模型拟合结果最优，幂函数（有截距）模型次之。而在使用检验数据进行估测时，幂函数（有截距）有着最好的估测效果。随机森林模型均具有较好的拟合效果，使用检验数据进行估测，不同竞争指数对模型拟合提升程度不同，与树冠重叠面积相关的竞争指数CI3取得了最好的效果。支持向量回归模型拟合优度小于随机森林，略大于传统模型。对胸径进行估测时，包含与竞争木大小相关的竞争指数CI4的模型为最优模型。 结论 传统模型和机器学习模型在拟合与估测单木胸径上均取得了一定的效果，利用机器学习模型效果更优。在模型的不同自变量组合中，加入有关树冠的竞争指数能使模型预测精度提高，决定系数R2增加，EMA、ERMS及AIC减小。传统模型的最优竞争指数为重叠内角相关的竞争指数CI2，在机器学习方法中与对象木和竞争木大小相关的竞争指数CI3和CI4也取得了较好的效果。此外，偏冠指数对于胸径估测的提升效果仍需进一步验证。 Abstract:Objective The rapid development of unmanned aerial vehicle remote sensing has provided a new direction for diameter at breast height (DBH) prediction. This study was suitable for extracting individual tree crown factors from sample plots through unmanned aerial vehicle remote sensing technology, estimating indicators such as DBH and stand basal area per hectare, and achieving accurate and efficient forest resource monitoring and management. Method Based on the ground survey data of 33 Cunninghamia lanceolata plantations in Jiangle National Forest Farm, Fujian Province of eastern China, ten traditional models and two machine learning methods were used to estimate the individual DBH. Based on different combinations of independent variables, the impact of different factors on the estimation of DBH was analyzed. Result According to the fitting results of traditional model parameters, it can be seen that the crown radius was significantly positively correlated with DBH, while the stand density, crown deviation factor, and competition index were all significantly negatively correlated with DBH. The optimal competition index introduced in the traditional model modeling process was CI2, which was related to the overlapping internal angles of tree crowns, and the fitting result of model power logistic model was the best, followed by the power function model (with intercept). The power function model (with intercept) had the best estimation effect when using test data for estimation. RF models all had high fitting effect. Using test data to estimate, different competition indices had varying degrees of improvement in model fitting, and the competition index CI3, which was related to the overlapping area of tree crowns, achieving the best effect. The goodness of fit of SVR model was less than that of random forest and slightly greater than traditional model. When estimating the DBH, the model containing competition index CI4 related to the size of competing trees was the optimal model. Conclusion Both traditional models and machine learning models have achieved certain results in fitting and estimating the DBH of individual trees, and the use of RF models is more effective. Adding competition indices related to tree crowns to different combinations of independent variables in the model can improve the prediction accuracy, increase the R2 and reduce EMA, ERMS, and AIC. The optimal competition index introduced for different models is the competition index CI2 related to overlapping internal angles, and in the machine learning methods, the competition indexes CI3 and CI4 related to the size of target trees and competing trees also achieve good results. The improvement effect of CAI on DBH estimation still needs further verification. -
Key words:
- DBH estimation /
- stand competition /
- random forest /
- support vector machine
-
图 1 竞争指数示意图
CI1 ~ CI4. 竞争指数，DOL. 对象木和竞争木之间树冠投影重叠的距离（m），RC. 树冠半径平均值，θ. 竞争木的重叠区域对对象木的圆的内角（弧度），RCmax. 最大树冠半径，Z. 影响区面积（其半径等于最大树冠的半径，m2），O. 竞争木和对象木之间的树冠重叠面积（m2）。下同。CI1−CI4, the competition index; DOL, the distance (m) between the crown projection overlaps of the target and the competitor; RC, average crown radius; θ. the overlapping area of the competitor affecting the internal angle (radian) of the target’s circle; RCmax, the maximum crown radius of the target; Z, area of influence area (whose radius is equal to the radius of the maximum tree crown, m2); O, the crown overlap area between the target and the competitor (m2). The same below.
Figure 1. Diagram of competition factors
图 2 随机森林模型特征变量相对重要性
Figure 2. Relative importance of RF models characteristic variables
表 1 建模数据和检验数据统计
Table 1. Summary statistics of modeling set and validation set
数据类型 Data type 建模数据 Modeling data 检验数据 Validation data 最小值
Min. value最大值
Max. value平均值
Mean标准差
Standard deviation最小值
Min. value最大值
Max. value平均值
Mean标准差
Standard deviationDBH/cm 9.20 39.20 21.89 4.97 10.00 38.80 21.72 5.19 树冠半径Crown radius/m 0.45 3.00 1.52 0.34 0.44 2.79 1.55 0.36 偏冠指数Crown asymmetry index 0.04 0.42 0.19 0.07 0.05 0.55 0.18 0.07 林分密度/（株·hm−2） Stand density//(tree·ha−1) 475.00 2 050.00 1 264.82 488.64 475.00 2 050.00 1 264.62 486.36 
下载: 导出CSV
表 2 传统模型形式
Table 2. Traditional model form
模型 Model 数学表达式 Mathematical expression 名称 Name M1 D = a + b × RC 线性函数 Linear function M2 D = a × RC^b 幂函数 Power function M3 D = a × exp(b × RC) 指数函数 Exponential function M4 D = a × (1 − exp(−b × RC)) 单分子式 Monomolecular function M5 D = a × b^RC 复合型 Composite function M6 D = exp(a + b × RC) 生长型 Growth function M7 D = (RC/(a + b × RC))^2 豪斯费尔德Ⅰ型 Hausfeld Type Ⅰ M8 D = a/(1 + b × exp(−c × RC)) 逻辑斯蒂函数 Logistic function M9 D = a + b × RC + c × RC^2 二次型 Quadratic function M10 D = a + b × RC^c 幂函数（有截距） Power function (with intercept) 注：D为单木胸径，RC为单木树冠半径，a、b、c均为模型参数。Notes: D represents the DBH of a single tree, RC represents the crown radius of a single tree, and a, b, and c are all model parameters.
下载: 导出CSV
表 3 传统模型最优变量组合形式
Table 3. Optimal variable combination forms of traditional model
模型 Model 含竞争指数 Including competitive factor 不含竞争指数 Excluding competitive factor M1 (a + b × CI2) + (c + d × SD) × RC a + (b + c × SD) × RC M2 (a + b × SD) × RC^(c + d × CI2) (a + b × SD) × RC^c M3 (a + b × SD) × exp((c + d × CI2) × RC) (a + b × SD) × exp(c × RC) M4 (a + b × SD) × (1 − exp((c + d × CI2) × (−RC))) (a + b × SD) × (1 − exp(c × (−RC))) M5 (a + b × SD) × (c + d × CI2)^RC (a + b × SD) × c^RC M6 exp((a + b × SD) + (c + d × CI2) × RC) exp((a + b × SD) + c × RC) M7 (RC/((a + b × CI3) + (c + d × SD) × RC))^2 (RC/(a + (b + c × SD) × RC))^2 M8 (a + b × SD)/(1 + (c + d × CI2) × exp((−RC) × (e + f × CAI))) (a + b × SD)/(1 + c × exp((−RC) × (d + e × CAI))) M9 (a + b × CI2) + (c + d × SD) × RC + (e + f × CAI) × RC^2 a + (b + c × SD) × RC + (d + e × CAI) × RC^2 M10 (a + b × CI2) + (c + d × SD) × RC^(e + f × CAI) a + (b + c × SD) × RC^(d + e × CAI) 注： SD. 林分密度，CAI. 偏冠指数，d、e、f 均为模型参数。Notes: SD, stand density. CAI, crown asymmetry index. d, e, and f are all model parameters.
下载: 导出CSV
表 4 传统模型参数估计
Table 4. Parameter estimation of traditional models
模型
Model竞争指数
Competitive
factor参数 Parameter a b c d e f M1 CI2 11.477（0.751）*** −1.069（0.255）*** 10.006（0.511）*** −0.002（0.000）*** 10.985（0.753）*** 10.102（0.519）*** −0.002（0.000）*** M2 CI2 21.520（0.533）*** −0.003（0.000）*** 0.548（0.040）*** −0.065（0.022）** 21.894（0.529）*** −0.003（0.000）*** 0.482（0.034）*** M3 CI2 16.373（0.645）*** −0.002（0.000）*** 0.327（0.022）*** −0.025（0.007）*** 16.914（0.656）*** −0.002（0.000）*** 0.297（0.020）*** M4 CI2 38.389（1.904）*** −0.005（0.001）*** 0.815（0.081）*** −0.055（0.016）*** 38.036（1.810）*** −0.005（0.001）*** 0.810（0.077）*** M5 CI2 16.388（0.645）*** −0.002（0.000）*** 1.385（0.030）*** −0.032（0.009）*** 16.914（0.656）*** −0.002（0.000）*** 1.346（0.028）*** M6 CI2 2.815（0.041）*** 0.000（0.000）*** 0.327（0.022）*** −0.025（0.007）*** 2.851（0.041）*** 0.000（0.000）*** 0.297（0.020）*** M7 CI3 0.076（0.006）*** 0.011（0.004）** 0.139（0.004）*** 0.000（0.000）*** 0.076（0.006）*** 0.140（0.004）*** 0.000（0.000）*** M8 CI2 54.886（19.461）** −0.007（0.003）** 2.642（1.003）** 0.251（0.075）*** 0.681（0.239）** −0.299（0.164） 56.805（23.159）* −0.008（0.004）* 2.759（1.180）* 0.657（0.259）* −0.359（0.184） M9 CI2 10.973（2.107）*** −1.013（0.255）*** 10.826（2.606）*** −0.002（0.000）*** 0.166（0.844） −2.337（0.945）* 10.439（2.131）*** 11.032（2.641）*** −0.002（0.000）*** 0.184（0.856） −2.637（0.955）** M10 CI2 4.178（7.384） −0.972（0.255）*** 17.865（7.620）* −0.003（0.000）*** 0.706（0.286）* −0.614（0.351） 0.463（10.094） 21.486（10.399）* −0.003（0.000）*** 0.600（0.287）* −0.591（0.353） 注：*为参数估计值显著（P < 0.05），**为中等显著（P < 0.01），***为极显著（P < 0.001），括号内数值为标准误。Notes: * implies that the parameter estimated value is significant (P < 0.05); ** implies that the parameter estimate is moderately significant (P < 0.01); and *** implies that the parameter estimate is extremely significant (P < 0.001). The values in brackets are standard errors.
下载: 导出CSV
表 5 传统模型拟合优度和检验结果
Table 5. Goodness of fit and test results of traditional model
模型
Model竞争指数
Competitive factor建模数据 Modeling data 检验数据 Validation data EMA/cm ERMS/cm R2 EMA/cm ERMS /cm R2 M1 CI2 3.017 3.738 0.439 2.946 3.799 0.444 3.063 3.792 0.421 2.997 3.889 0.417 M2 CI2 3.032 3.744 0.438 2.977 3.830 0.435 3.055 3.775 0.428 3.000 3.897 0.415 M3 CI2 3.018 3.735 0.441 2.952 3.817 0.439 3.050 3.779 0.427 2.994 3.900 0.415 M4 CI2 3.044 3.769 0.431 2.980 3.849 0.430 3.083 3.811 0.418 3.037 3.922 0.408 M5 CI2 3.019 3.736 0.440 2.953 3.819 0.439 3.050 3.779 0.427 2.994 3.900 0.415 M6 CI2 3.019 3.735 0.440 2.951 3.816 0.440 3.050 3.779 0.427 2.995 3.897 0.416 M7 CI3 3.065 3.798 0.422 3.007 3.859 0.427 3.097 3.83 0.412 3.040 3.922 0.408 M8 CI2 2.992 3.695 0.452 2.927 3.798 0.444 3.023 3.740 0.439 2.984 3.886 0.418 M9 CI2 3.005 3.715 0.446 2.940 3.791 0.446 3.044 3.769 0.430 2.998 3.877 0.421 M10 CI2 2.995 3.703 0.450 2.927 3.792 0.446 3.035 3.752 0.435 2.991 3.879 0.420 注： EMA. 平均绝对误差，ERMS. 均方根误差，R2. 决定系数。Notes: EMA, mean absolute error, ERMS, root mean square error, R2, coefficient of determination.
下载: 导出CSV
表 6 随机森林模型参数
Table 6. Goodness of fit and test results of RF Model
模型
Model参数 Parameter 变量组合
Variable combination决策树
Decision tree特征数
Feature numberRF1 RC + SD 172 2 RF2 RC + SD + CAI 143 3 RF3 RC + SD + CAI + CI1 456 4 RF4 RC + SD + CAI + CI2 330 4 RF5 RC + SD + CAI + CI3 287 4 RF6 RC + SD + CAI + CI4 264 4
下载: 导出CSV
表 7 随机森林拟合优度和检验结果
Table 7. Goodness of fit and test results for RF
模型
Model建模数据 Modeling data 检验数据 Validation data EMA/cm ERMS/cm R2 AIC EMA/cm ERMS/cm R2 AIC RF1 1.604 2.011 0.852 764.347 2.782 3.575 0.533 470.271 RF2 1.399 1.769 0.895 626.737 2.706 3.447 0.564 458.883 RF3 1.282 1.625 0.914 536.379 2.700 3.382 0.578 453.918 RF4 1.290 1.646 0.914 549.956 2.649 3.340 0.590 449.396 RF5 1.313 1.675 0.909 569.191 2.665 3.329 0.591 448.201 RF6 1.325 1.690 0.909 578.672 2.709 3.404 0.571 456.345 注： AIC. 赤池信息准则。Note: AIC, akaike information criterion.
下载: 导出CSV
表 8 支持向量回归模型参数
Table 8. Parameters of SVR model
模型 Model 变量组合 Variable combination 核函数 Kernel function 惩罚系数 Cost coefficient 内核系数 Gamma coefficient 距离误差 Epsilon SVR1 RC + SD RBF 5 0.01 0.5 SVR2 RC + SD + CAI RBF 10 0.01 1 SVR3 RC + SD + CAI + CI1 RBF 10 0.01 0.5 SVR4 RC + SD + CAI + CI2 RBF 1 0.1 0.5 SVR5 RC + SD + CAI + CI3 RBF 1 0.1 0.5 SVR6 RC + SD + CAI + CI4 RBF 5 0.01 0.5
下载: 导出CSV
表 9 支持向量回归拟合统计量
Table 9. Fitting statistics of SVR model
模型
Model建模数据 Modeling data 检验数据 Validation data EMA/cm ERMS/cm R2 AIC EMA/cm ERMS/cm R2 AIC SVR1 3.010 3.726 0.444 1435.174 2.967 3.908 0.413 502.849 SVR2 3.029 3.700 0.454 1429.429 3.002 3.880 0.421 502.240 SVR3 2.928 3.616 0.476 1406.466 2.908 3.798 0.445 496.451 SVR4 2.829 3.498 0.510 1370.394 2.919 3.792 0.446 495.886 SVR5 2.825 3.507 0.509 1373.136 2.919 3.789 0.447 495.503 SVR6 2.917 3.614 0.478 1405.872 2.844 3.753 0.459 492.013
下载: 导出CSV
-
[1] 邓坤枚, 邵彬, 李飞. 长白山北坡云冷杉林胸径、树高结构及其生长规律的分析[J]. 资源科学, 1999, 21(1): 79−86.Deng K M, Shao B, Li F. Analysis for diameter, height structures and growth of spruce-fir forest on northern slope of Changbai Mountains[J]. Resource Science, 1999, 21(1): 79−86. [2] Bi H Q, Turner J, Lambert M J. Additive biomass equations for native eucalypt forest trees of temperate Australia[J]. Trees, 2004(4): 467−479. [3] Zhou X H, Brandle J R, Schoeneberger M M, et al. Developing above-ground woody biomass equations for open-grown, multiple-stemmed tree species: shelterbelt-grown Russian-olive[J]. Ecological Modelling, 2007, 202(3): 311−323. [4] 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. [5] 单凯丽, 臧颢, 潘萍, 等. 赣中天然闽楠单木冠幅预测模型的研究[J]. 南京林业大学学报: 自然科学版, 2022, 46(1): 88−96.Shan K L, Zang H, Pan P, et al. Individual tree crown width prediction models for natural Phoebe bournei in central Jiangxi Province[J]. Journal of Nanjing Forestry University (Natural Sciences Edition), 2022, 46(1): 88−96. [6] 陈周娟, 程光, 卜元坤, 等. 基于无人机倾斜影像的阔叶林单木参数提取[J]. 林业资源管理, 2022 (1): 132−141.Chen Z J, Cheng G, Bu Y K, et al. Single tree parameter extraction of broad-leaved forest based on UAV tilting photography [J]. Forestry Resource Management, 2022 (1): 132−141. [7] 奚祥书 , 夏凯, 杨垠晖 , 等. 结合多光谱影像降维与深度学习的城市单木树冠检测[J]. 遥感学报, 2022, 26(4): 711−721. doi: 10.11834/jrs.20220163Xi X S, Xia K, Yang Y H, et al. Urban individual tree crown detection research using multispectral image dimensionality reduction with deep learning[J]. National Remote Sensing Bulletin, 2022, 26(4): 711−721. doi: 10.11834/jrs.20220163 [8] 冉崇宪, 李森磊. 利用无人机多光谱影像提取树冠信息[J]. 测绘通报, 2022 (7): 112−117.Ran C X, Li S L. Tree canopy delineation using UAV multispectral imagery[J]. Bulletin of Surveying and Mapping, 2022(7): 112−117. [9] 谢运鸿, 荆雪慧, 孙钊, 等. 基于实例分割的高郁闭度林分单木树冠无人机遥感提取[J]. 林业科学研究, 2022, 35(5): 14−21.Xie Y H, Jing X H, Sun Z, et al. Tree crown extraction of UAV remote sensing high canopy density stand based on instance segmentation[J]. Forest Research, 2022, 35(5): 14−21. [10] 韦雪花, 王佳, 冯仲科. 北京市13个常见树种胸径估测研究[J]. 北京林业大学学报, 2013: 35 (5): 56−63.Wei X H, Wang J, Feng Z K. Estimating diameter at breast height for thirteen common tree species in Beijing[J]. Journal of Beijing Forestry University, 2013: 35 (5): 56−63. [11] 陈瑞波, 朱宁宁, 梅树红, 等. 广西桉树和马尾松单木胸径/冠幅−树高模型构建[J]. 测绘与空间地理信息, 2022, 45(7): 70−73, 84.Chen R B, Zhu N N, Mei S H, et al. Individual diameter-height and crown-height prediction models for Pinus massoniana and Eucalyptus in Guangxi[J]. Geomatics & Spatial Information Technology, 2022, 45(7): 70−73, 84. [12] 洪李斌, 卿蕴贤, 田佳赫, 等. 基于混合效应模型的塞罕坝华北落叶松人工林单木去皮胸径生长预测[J]. 林业与生态科学, 2022, 37(2): 127−133.Hong L B, Qing Y X, Tian J H, et al. Prediction of single tree inside bark DBH growth of Larix principis-rupprechtii plantation in Saihanba based on mixed effects model [J]. Forestry and Ecological Sciences, 2022, 37(2): 127−133. [13] 谢伊, 杨华. 长白山天然云冷杉针阔混交林主要树种胸径生长与林分空间结构的关系[J]. 北京林业大学学报, 2022, 44(9): 1−11. doi: 10.12171/j.1000-1522.20210280Xie Y, Yang H. Relationship between stand spatial structure and DBH increment of principal species in natural spruce-fir mixed forest in Changbai Mountains of northeastern China[J]. Journal of Beijing Forestry University, 2022, 44(9): 1−11. doi: 10.12171/j.1000-1522.20210280 [14] 王孝安, 段仁燕, 王明利. 太白红杉单木胸径生长模型的研究[J]. 武汉植物学研究, 2005, 23(2): 157−162.Wang X A, Duan R Y, Wang M L. Study on DBH increment model of individual trees growing for Larix chinensis[J]. Journal of Wuhan Botanical Research, 2005, 23(2): 157−162. [15] 陆江. 林分内竞争对林木胸径生长量的影响研究[J]. 林业调查规划, 2021, 46(2): 153−156, 164. doi: 10.3969/j.issn.1671-3168.2021.02.028Lu J. Effect of intra-stand competition on tree DBH growth[J]. Forestry Inventory and Planning, 2021, 46(2): 153−156, 164. doi: 10.3969/j.issn.1671-3168.2021.02.028 [16] 刘强, 李凤日, 董利虎. 基于竞争因子的落叶松人工林单木生长模型[J]. 植物研究, 2014: 34 (4): 547−553.Liu Q, Li F R, Dong L H. Individual tree growth model of larch plantation based on crown competition factors[J]. Bulletin of Botanical Research, 2014: 34 (4): 547−553. [17] 张晔珵, 张怀清, 陈永富, 等. 基于树冠因子的林木竞争指数研究[J]. 林业科学研究, 2016: 29 (1): 80−84.Zhang Y C, Zhang H Q, Chen Y F, et al. Study of tree competition index based on crown feature[J]. Forest Research, 2016: 29 (1): 80−84. [18] 雷相东. 机器学习算法在森林生长收获预估中的应用[J]. 北京林业大学学报, 2019, 41(12): 23−36. doi: 10.12171/j.1000-1522.20190356Lei X D. Application of machine learning algorithms in forest growth and yield prediction[J]. Journal of Beijing Forestry University, 2019, 41(12): 23−36. doi: 10.12171/j.1000-1522.20190356 [19] 梁瑞婷, 孙玉军, 李芸. 深度学习和传统方法模拟杉木树高−胸径模型比较[J]. 林业科学研究, 2021, 34(6): 65−72.Liang R T, Sun Y J, Li Y. Comparison of deep learning and traditional models to simulate the height-DBH relationship of Chinese Fir[J]. Forest Research, 2021, 34(6): 65−72. [20] 张孟库, 姜立春. 基于机器学习的落叶松树皮厚度预测[J]. 北京林业大学学报, 2022, 44(6): 54−62.Zhang M K, Jiang L C. Prediction of bark thickness for Larix gmelinii based on machine learning[J]. Journal of Beijing Forestry University, 2022, 44(6): 54−62. [21] 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 Q X, 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. [22] Che H S, Tan X H, Xiang C W, et al. Stand basal area modelling for Chinese fir plantations using an artificial neural network model[J]. Journal of Forestry Research, 2019, 30(5): 1641–1649. doi: 10.1007/s11676-018-0711-9 [23] 孙钊, 潘磊, 乔晶晶, 等. 偏冠对树冠垂直投影面积计算的影响[J]. 林业科学研究, 2022, 35(1): 166−171.Su Z, Pan L, Qiao J J, et al. Effect of partial crown on calculation of vertical projection area of crown[J]. Forest Research, 2022, 35(1): 166−171. [24] Zhou M L, Lei X D, Lu J, et al. Comparisons of competitor selection approaches for spatially explicit competition indices of natural spruce-fir-broadleaf mixed forests[J]. European Journal of Forest Research, 2022, 141: 177−211. doi: 10.1007/s10342-021-01430-8 [25] Ou Q X, Lei X D, Shen C C. Individual tree diameter growth models of larch-spruce-fir mixed forests based on machine learning algorithms[J/OL]. Forests, 2019, 10(2): 187[2023−01−02]. https://doi.org/10.3390/f10020187. [26] Malone T, Liang J J. A bark thickness model for white spruce in Alaska northern forests[J/OL]. International Journal of Forestry Research, 2014, 2009: 1−5[2023−01−02]. https://doi.org/10.1155/2009/876965. [27] 何亚平, 费世民, 徐嘉, 等. 川西南山地云南松林窗边界木偏冠现象与影响因素[J]. 北京林业大学学报, 2007, 29(6): 66−71.He Y P, Fei S M, Xu J, et al. Crown inclination of Pinus yunnanensis gap border trees and the influencing factors in the mountain area of southwest of Sichuan, southwestern China[J]. Journal of Beijing Forestry University, 2007, 29(6): 66−71. -
点击查看大图
图(2) / 表(9)
计量
- 文章访问数: 41
- HTML全文浏览量: 8
- PDF下载量: 13
- 被引次数: 0
