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 |
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 |
?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 |
?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. |
?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. |
?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 |
?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 |
?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 |
?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. |
?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 |