Stand carbon stock growth model system for Larix olgensis plantation
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摘要:
目的 目前关于林分碳储量随年龄动态变化的模型研究较少，本研究通过建立林分水平的碳储量生长模型系，为区域尺度的森林碳储量动态预估提供方法。 方法 以吉林省长白落叶松人工林为对象，使用立地质量分级算法将所有样地划分为3个立地等级，并将其作为哑变量引入模型系中，使用联立方程组的方法将林分平均高、断面积生长模型和林分碳储量模型3个方程进行联合估计，建立林分碳储量生长模型系。采用调整确定系数（ $ {{R}}_{{\text{adj}}}^2 $ ）、估计值的标准误（SEE）和平均预估误差（MPE）来评价模型的表现，分析不同立地等级和林分密度指数（SDI）下林分碳储量的生长过程，及林分断面积和平均高对林分碳储量的影响。结果 （1）林分碳储量生长模型系中林分平均高生长模型、林分断面积生长模型和林分碳储量模型的 $ {{R}}_{{\text{adj}}}^2 $ 分别为0.879、0.977和0.953，MPE均 < 2%，具有较好的拟合优度。（2）直接利用林分平均高和断面积或由生长模型得到林分平均高和断面积的这两种途径都可以准确估计林分碳储量，结果仅相差0.02 t/hm2，模型系具有良好的通用性与稳定性。（3）林分碳储量生长量随立地质量的提高而增加；立地等级相同时，SDI < 1 500株/hm2时生长较慢，SDI > 1 500株/hm2时，在40年以后的林分密度对碳储量生长过程基本无影响；林分密度指数控制在1 500 ~ 2 000株/hm2时可实现较快的碳储量生长。（4）林分碳储量随林分断面积和平均高的增加而增加，林分断面积与林分碳储量的关系更为密切。结论 林分碳储量的生长和立地等级、林分平均年龄、密度、断面积、平均高等因子有密切联系，采用联立方程组方法是建立林分碳储量生长模型系的有效方法。本研究建立的林分碳储量生长模型系可以对林分碳储量动态进行有效预测，为了解林分碳储量的生长过程和森林碳汇评估提供了工具。 Abstract:Objective There are knowledge gaps on stand carbon stock growth model at present. This study developed a stand-level carbon stock growth model system to provide a method for dynamic estimation of regional forest carbon storage with time. Method Taking Larix olgensis plantation in Jilin Province of northeastern China as the research object, the site quality classification algorithm was used to divide all sample plots into three site grades, which were introduced into the model system as dummy variables. The stand carbon stock growth model system was established by simultaneous equations to link stand average height, basal area growth model and stand carbon stock model. The adjusted coefficient of determination ( $ {{R}}_{{\text{adj}}}^2 $ ), the standard error of the estimated value (SEE) and the average prediction error (MPE) were used to evaluate model performance. The growth process of stand carbon stock under different site grades and stand density index (SDI), and the influence of stand basal area and average height on stand carbon stock were analyzed.Result (1) The $ {{R}}_{{\text{adj}}}^2 $ of stand average height growth model, basal area growth model and carbon stock model were 0.892, 0.979 and 0.960, respectively, and the MPEs were both less than 2%. (2) Both procedures in the model system (inventory- and model-derived stand average height and basal area) could accurately estimate the stand carbon stock, and the difference was only 0.02 t/ha, so the model system had great generality and stability. (3) Stand carbon stock growth increased with the increasing site grade of sample plots. When the site grade was the same, the growth was slow with SDI less than 1 500 plant/ha; but there were no differences in the growth process among different SDIs larger than 1 500 plant/ha after 40 years, and the optimal SDI for maximum stand carbon stock was about 1 500−2 000 plant/ha. (4) The stand carbon stock increased with the increase of stand basal area and average height, and stand basal area had larger effects on stand carbon than stand average height.Conclusion The growth of stand carbon stock is closely related to the site grade, stand average age, density, basal area and average height. The modeling approach of simultaneous equations is a feasible method for developing the stand carbon stock growth model system. The stand carbon stock growth model system developed by this study could effectively predict stand carbon stock, which providing a tool for understanding the growth of stand carbon stock and forest carbon sink assessment. -
Key words:
- stand carbon stock model /
- growth process /
- site grade /
- stand density /
- Larix olgensis plantation
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图 1 吉林省落叶松人工林样地分布图
Figure 1. Distribution of sample plots of larch plantation in Jilin Province
图 3 林分碳储量与林分断面积、平均高的关系
Figure 3. Relationship between stand carbon stock andstand basal area as well as average height
表 1 林分因子概况(n = 150)
Table 1. Summary statistics of stand variables (n = 150)
变量 Variable 平均值 Mean 最小值 Min. 最大值 Max. 标准差 SD 林分平均高 Stand average height (H)/m 13.2 5.0 22.0 3.8 林分公顷断面积/(m2·hm−2) Stand basal area (Ba)/(m2·ha−1) 13.41 3.67 27.97 6.28 林分公顷蓄积/(m3·hm−2) Stand volume (V)/(m3·ha−1) 90.75 16.92 229.78 49.97 平均胸径 Average DBH (Dg)/cm 13.6 6.7 26.1 3.8 林分碳储量/(t·hm−2) Stand carbon stock (C)/(t·ha−1) 37.64 8.11 91.79 19.80 林分密度指数/(株·hm−2) Stand density index (SDI)/(tree·ha−1) 494 159 1 086 212 林分平均年龄/a Stand average age (A)/year 30 11 50 10 
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表 2 不同立地等级的林分平均高生长模型结果
Table 2. Results of stand average height growth model with different site grades
模型 Model 参数值 Parameter 标准差 SD $ {{R}}_{{\text{adj}}}^2 $ SEE/m MPE/% $ {{\hat H}} = {a_{}}{\left[ {1 - \exp\left( -\left(\displaystyle\sum {{b_i} \cdot {\text{SIT}}{{\text{E}}_i}} \right){A}\right)} \right]^{{\text{ }}c}} $ (i = 1, 2, 3) a = 27.247 3.800 0.889 1.261 1.547 b1 = 0.027 0.011 b2 = 0.019 0.007 b3 = 0.012 0.004 c = 0.789 0.107
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表 3 划分立地等级后的样地林分因子概况
Table 3. A summary of stand factor characteristics after site classification
林分因子 Stand factor 立地等级 Site grade 样地数 Sample plot number 平均值 Mean 最小值 Min. 最大值 Max. 标准差 SD F H 1 38 16.7a 11.0 22.0 2.9 55.652 2 70 13.2b 7.0 19.0 3.0 3 42 9.9c 5.0 15.0 2.5 Ba 1 38 16.58a 6.22 27.09 4.96 17.547 2 70 14.16b 3.79 27.97 6.61 3 42 9.29c 3.67 19.90 4.45 C 1 38 48.53a 15.90 87.69 16.96 19.417 2 70 39.69b 9.29 91.79 20.39 3 42 24.36c 8.11 54.95 12.95 注：H、Ba、C的单位分别为m、m2/hm2、t/hm2。不同小写字母表示各林分因子在不同立地等级下的差异显著(P < 0.05)。Notes: the units of H, Ba, C are m, m2/ha, t/ha, respectively. Different lowercase letters indicate significant differences for varied stand factors under different site grades (P < 0.05).
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表 4 林分碳储量生长模型式(1)的结果
Table 4. Results of growth model equation (1) of stand carbon stock
模型 Model 参数值 Parameter value 标准差 SD $ {{R}}_{{\text{adj}}}^2 $ SEE/(t·hm−2) SEE/(t·ha−1) MPE/% ${{\hat C}} = \left( {\displaystyle\sum {{a_i} \cdot {\rm{SIT}}{{\rm{E}}_i}} } \right){\left[ {1 - \exp ( - {b_1}{{\left( {\dfrac{{{\rm{SDI}}}}{{1\;000}}} \right)}^{{b_2}}} \cdot {{A}})} \right]^{{\rm{ }}c}}(i = 1, 2, 3) $ a1 = 155.893 45.193 0.962 3.876 1.662 a2 = 145.708 41.691 a3 = 120.919 34.778 b1 = 0.012 ns 0.008 b2 = 1.23 0.109 c = 0.561 0.038 注：ns表示模型参数在0.05水平不显著。Note: ns indicates that parameters of the model are not significant at 0.05 level.
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表 5 独立林分断面积生长模型结果
Table 5. Growth model results of independent stand basal area
模型 Model 参数值 Parameter value 标准差 SD $ {{R}}_{{\text{adj}}}^2 $ SEE/(m2·hm−2) SEE/(m2·ha−1) MPE/% $ \widehat {{\text{Ba}}} = {a_{}}{\left[ {1 - \exp\left( - {b_1}{{\left(\dfrac{{{\text{SDI}}}}{{1\;000}}\right)}^{{b_2}}} \cdot {{A}}\right)} \right]^{{\text{ }}c}} $ a = 32.340 2.232 0.979 0.911 1.097 b1 = 0.023 0.007 b2 = 3.888 0.268 c = 0.275 0.019
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表 6 林分碳储量生长模型系的参数估计与刀切法验证结果
Table 6. Parameter estimation on growth model system of stand carbon stock and validation results by jackknife method
模型 Model 参数 Parameter 平均值 Mean 最小值 Min. 最大值 Max. 标准差 SD ${{R} }_{ {\text{adj} } }^2 $ SEE MPE/% 林分平均高生长模型
Stand average height growth model (4-1)a1 29.010 26.866 31.869 0.491 0.889 1.261 1.548 b11 0.022 0.017 0.028 0.001 b12 0.016 0.013 0.020 0.001 b13 0.009 0.007 0.012 0.000 c1 0.747 0.716 0.820 0.010 林分断面积生长模型
Stand basal area growth model (4-2)a2 32.171 31.051 34.333 0.286 0.979 0.912 1.097 b21 0.023 0.017 0.027 0.001 b22 3.863 3.791 3.948 0.023 c2 0.275 0.267 0.281 0.002 林分碳储量模型
Stand carbon stock model (4-3)d1 4.867 4.762 5.028 0.026 0.957 4.108 1.762 d2 10.124 9.593 10.972 0.134 注：模型4-1、4-2、4-3的SEE单位分别为m、m2/hm2、t/hm2。Notes: the SEE units of model 4-1, 4-2 and 4-3 are m, m2/ha and t/ha, respectively.
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表 7 2种林分碳储量生长模型系林分碳储量估计途径的结果
Table 7. Estimation results of stand carbon stock by different methods using stand carbon stock growth model system
龄组 Age group 途径1/(t·hm−2) Method 1/(t·ha−1) 途径2/(t·hm−2) Method 2/(t·ha−1) 相对差异 Relative difference/% 幼龄林 Young stand 25.93 26.32 1.51 中龄林 Middle-aged stand 32.84 32.46 −1.17 近熟林 Near-mature stand 44.43 44.19 −0.54 成熟林 Mature stand 53.00 53.89 1.67 总体 Total 37.51 37.53 0.07 注：建模样本中没有过熟林。Note: there are no over-mature stand in modeling samples.
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