Height curve of natural Larix gmelinii in the Daxing’anling Mountains of northeastern China based on forest classification
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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。 方法 以大兴安岭地区翠岗林场56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（R2 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。 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方程的参数a和b上时，模型的拟合效果最好,其中兴安落叶松树高曲线模型的调整系数（R2 adj）、均方根误差（RMSE）和赤池信息量（AIC）分别为0.858 8、1.642 4和2 081.902；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（即τ = 0.5），其树高曲线的3个统计量则依次为0.849 8、1.693 8和2 211.037。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。 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。 Abstract:Objective The 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. Method Based 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 (R2 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 gmelinii was 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 gmelinii were further evaluated and compared. Result The optimal basic model of Larix gmelinii height 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. R2 adj, RMSE and AIC of Larix gmelinii tree 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. Conclusion The height curve model of Larix gmelinii in 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 gmelinii in the Daxing’anling Mountains region. -
Key words:
- tree classification /
- quantile regression /
- dummy variable /
- tree height curve
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图 1 不同林木等级的兴安落叶松残差分布
Figure 1. Residual distribution of Larix gmelinii under different tree grades
图 2 不同分位数兴安落叶松树高−胸径曲线模拟
Figure 2. Tree height-DBH curve simulation of Larix gmelinii based on base model, median model and different quantile groups
图 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
表 1 样地基本特征
Table 1. Basic characteristics of the sample plots
落叶松蓄积占比
Percentage of larch volume样地数量
Number of sample plot变量
Variable最小值
Min. value最大值
Max. value平均值
Mean标准差
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−2）
Stand density/(tree·ha−1)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−2）
Stand density/(tree·ha−1)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−2）
Stand density/(tree·ha−1)800.0 2 090.0 1 373.3 353.8 25.8 
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表 2 天然兴安落叶松不同等级林木的样本统计量
Table 2. Sample statistics of different grades of natural Larix gmelinii
林木分级
Tree classification分组
Group样本数
Number of sample plotDBH/cm 树高 Tree height/m 最小值
Min. value平均值
Mean最大值
Max. value最小值
Min. value平均值
Mean最大值
Max. value优势木 Dominant tree 建模数据 Modeling data 726 9.8 16.9 35.5 6.4 14.1 24.6 检验数据 Validation data 311 9.7 16.8 33.1 6.8 14.2 22.3 平均木 Average tree 建模数据 Modeling data 485 6.6 9.8 20.7 5.8 10.6 18.0 检验数据 Validation data 208 6.7 9.6 15.8 6.1 10.6 18.2 被压木 Pressed tree 建模数据 Modeling data 863 1.0 4.7 10.8 1.5 6.0 17.2 检验数据 Validation data 370 1.0 4.7 15.8 1.4 6.1 15.0
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表 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 表达式 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, b and c are model parameters.
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表 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 natural Larix gmelinii
等级
Grade模型
Model参数 Parameter 拟合精度 Fitting accuracy a b c R2 adj RMSE AIC 优势木
Dominant treeWykoff 3.203 4 −11.432 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 平均木
Average treeWykoff 3.073 8 −9.161 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 被压木
Pressed treeWykoff 2.717 8 −6.431 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下渐进t检验不显著。Notes: * indicates that the asymptotic for the parameter is not significant at the 0.05 level.
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表 5 不同参数组合哑变量树高−胸径模型拟合优度与评价指标
Table 5. Goodness of fit and evaluation index of dummy variable model with different parameter combinations
参数 Parameter R2 adj RMSE AIC a 0.848 8 1.699 7 2 225.612 a、b 0.858 8 1.642 4 2 081.902
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表 6 哑变量添加在a、b上的参数
Table 6. Parameters of dummy variable added to a and b
参数
Parametera0 a1 a2 b0 b1 b2 估计值
Estimated value2.689 9 0.490 5 0.410 3 −6.328 8 −4.772 9 −3.157 3
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表 7 分位数回归模型的参数估计
Table 7. Parameter estimation of quantile regression model
分位数
Quantile (τ)a b R2 adj RMSE AIC 0.1 2.906 7 −10.193 5 0.615 4 2.673 3 4 123.071 0.3 2.967 1 −9.020 3 0.810 0 1.905 2 2 703.786 0.5 3.008 2 −8.401 5 0.849 8 1.693 8 2 211.037 0.7 3.068 2 −7.982 1 0.814 9 1.880 5 2 649.209 0.9 3.150 5 −7.373 0 0.583 3 2.821 1 4 348.549
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表 8 分位数回归模型的拟合与评价
Table 8. Fitting and evaluation of quantile regression model
等级
Grade分位数
Quantile (τ)拟合精度 Fitting accuracy R2 adj RMSE AIC 优势木
Dominant tree0.1 −0.448 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 −0.279 4 3.188 0 1 686.427 平均木
Average tree0.1 −0.624 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 −0.979 2 3.051 1 1 085.027 被压木
Pressed tree0.1 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 of Larix gmelinii. The same below.
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表 9 兴安落叶松不同方法的树高−胸径模型独立性检验
Table 9. Validation statistics for tree height-DBH models of Larix gmelinii based on different methods
等级
Grade模型
ModelMAE MAPE 优势木
Dominant tree分位数模型
Quantile regression1.550 7 11.304 1 哑变量模型
Dummy variable model1.522 9 11.258 4 基础模型
Basic model1.561 4 11.400 5 平均木
Average tree分位数模型
Quantile regression1.461 8 13.778 2 哑变量模型
Dummy variable model1.383 4 14.126 9 基础模型
Basic model1.404 1 14.588 5 被压木
Pressed tree分位数模型
Quantile regression1.137 7 20.336 1 哑变量模型
Dummy variable model0.800 2 13.578 2 基础模型
Basic model0.907 9 16.265 0
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