Scientia Silvae Sinicae ›› 2020, Vol. 56 ›› Issue (11): 73-86.doi: 10.11707/j.1001-7488.20201108
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Bin Wang,Xianglin Tian,Tianjian Cao*
Received:
2020-01-16
Online:
2020-11-25
Published:
2020-12-30
Contact:
Tianjian Cao
CLC Number:
Bin Wang,Xianglin Tian,Tianjian Cao. Uncertainty Analysis of Height Predictions for Young Pinus tabulaeformis Using a Bayesian Approach[J]. Scientia Silvae Sinicae, 2020, 56(11): 73-86.
Fig.1
The locations of sampling plots and the distributions of height of the selected young trees in Qinling Mountains The 90 m-DEM (digital elevation models) was downloaded from the CGIAR-CSI GeoPortal (http://srtm.csi.cgiar.org). Qinling Mountains was drawn based on ecological area published by the World Wildlife Fund (WWF). Subplot of Fig. 1 for a, b and c is frequency of young trees of P. tabulaeformis for three forest regions. The vertical axis represents height class, and the horizontal axis represent the frequency of young trees."
Table 1
Statistics of young P. tabulaeformis plots"
项目Item | 林分平均高 Mean height (HD)/m | 林分平均胸径 Mean DBH (Dg)/cm | 林分密度 Stand density (SD)/hm-2 | 林分断面积 Basal area (BA)/(m2·hm-2) | 林分蓄积 Volume (V)/(m3·hm-2) | 幼树树高 Height of tree (HT)/m |
平均值Mean | 12.32 | 18.40 | 1 059 | 23.25 | 143.31 | 1.75 |
标准差SD | 2.79 | 4.07 | 487 | 7.81 | 61.98 | 0.69 |
最小值Min. | 7.20 | 10.41 | 353 | 11.50 | 55.66 | 0.37 |
最大值Max. | 17.30 | 27.70 | 2 400 | 48.96 | 286.12 | 3.30 |
变异系数Cofficient of variation(%) | 22.65 | 22.12 | 45.99 | 33.59 | 43.00 | 39.43 |
Table 2
Height models for young P. tabulaeformis"
序号 No | 模型类型 Model type | 模型结构Model structure | 贝叶斯信息 准则BIC | 均方根误差 RMSE |
1 | 线性 Linear | HTG=β0+β1×SL×cos(ASP)-β2×SL×sin(ASP)-β3×SL+β4× ln(HT)+β5×CCF+β6×LI+ε | 131.86 | 0.266 2 |
2 | HTG=β0+β1×SL×cos(ASP)-β2×SL×sin(ASP)-β3×SL+β4×HT+β5×HT2+β6 ln(CCF)+β7×LI+ε | 129.31 | 0.265 3 | |
3 | 对数线性 Log-linear | ln(HTG)=β0+β1×SL×cos(ASP)-β2×SL×sin(ASP)-β3×SL+β4×ln(HT)+β5×CCF+β6×LI+ε | 128.87 | 0.256 3 |
4 | ln(HTG)=β0+β1×SL×cos(ASP)-β2×SL×sin(ASP)-β3×SL+β4×ln(HT)+β5×ln(CCF)+β6×LI+ε | 126.75 | 0.223 4 | |
5 | 非线性 Nonlinear | HTG=exp[β0+β1×SL×cos(ASP)+β2×SL×sin(ASP)+β3×SL+β4×HT+β5×ln(HT)+β6×CCF+β7×LI]+ε | 127.13 | 0.241 1 |
6 | HTG=exp[β0+β1×SL×cos(ASP)-β2×SL×sin(ASP)-β3×SL+β4× HT+β5×HT2+β6×CCF+β7×LI]+ε | 128.78 | 0.249 4 |
Fig.2
95% credible intervals of 5-year height increment model due to parameter uncertainty and total uncertainty x axis represents each young P. tabulaeformis tree sample. The black dots represent observations of each young P. tabulaeformis, and the grey shade region represents the 95% Bayesian credible interval."
Table 3
Summary of equivalence-based regression results for height model of young P. tabulaeformis"
5年树高生长量 5-year height increment/cm | 样本量Number (n) | 置信区间 Confidence interval | 等效区间 Equivalent interval | 拒绝非相似的原假设 Reject dissimilarity | |||
Cβ- | Cβ+ | Iβ- | Iβ+ | ||||
截距Intercept(β0) | 66 | 0.58 | 0.72 | 0.44 | 0.74 | 是Yes | |
斜率Slope(β1) | 66 | 0.76 | 1.21 | 0.75 | 1.25 | 是Yes |
Table 4
Posterior probability distribution of parameters in the height model of young P. tabulaeformis"
参数 Parameter | 变量 Variable | 最大后验概率 MAP | 均值 Mean | 标准差 SD | 95%可信区间95% CI | |
下限Lower | 上限Upper | |||||
β0 | 截距Intercept | 0.412 | 0.425 | 0.372 | -0.311 | 1.160 |
β1 | SL×cos(ASP) | 0.355 | 0.331 | 0.084 | 0.166 | 0.496 |
β2 | SL×sin(ASP) | 0.070 | 0.070 | 0.056 | -0.041 | 0.182 |
β3 | SL | 0.153 | 0.169 | 0.184 | -0.195 | 0.533 |
β4 | ln(HT) | 0.571 | 0.570 | 0.083 | 0.446 | 0.693 |
β5 | ln(CCF) | -0.107 | -0.108 | 0.075 | -0.255 | -0.040 |
β6 | LI | -0.717 | -0.713 | 0.134 | -0.980 | -0.448 |
Fig.5
Height increment on 5-year height increment of young P. tabulaeformis based on HT, CCF, LI, and SL The grey shaded region represented 95% credible interval of Bayesian prediction, black lines represented mean ± one standard deviation, and black dot represented prediction by Bayesian MAP estimation. For Fig. 5a, the aspect (ASP) is 200°, the crown competition factor(CCF)is 150, the light interception(LI)is 0.6, slope (SL) is 35°. For Fig. 5b, the aspect (ASP) is 200°, the crown competition factor(CCF)is 150, the current height(HT)is 2 m, and the slope (SL) is 35°. For Fig. 5c, the aspect (ASP) is 200°, the crown competition factor(CCF)is 150, the current height(HT)is 2 m, and the light interception(LI)is 0.6. For Fig. 5d, the aspect (ASP) is 200°, the current height(HT)is 2 m, the light interception(LI)is 0.6, and the slope (SL) is 35°."
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